# Katedra Algorytmów i Modelowania Systemów

## Publikacje

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• ### 2018

• #### ANALIZA MOŻLIWOŚCI WYKORZYSTANIA TRANSFORMACJI FALKOWEJ DO DETEKCJI NIEZAJĘTYCH PASM CZĘSTOTLIWOŚCI

K. Bronk, D. Rutkowski, B. Wereszko, K. Wereszko, K. Żurek - Przegląd Telekomunikacyjny + Wiadomości Telekomunikacyjne - 2018
Celem pracy była implementacja oraz wykonanie badań efektywności wybranej metody wykrywania niezajętych zasobów częstotliwości, opartej na wyznaczaniu entropii sygnału z wykorzystaniem analizy falkowej. W referacie przedstawiono podstawy teoretyczne rozważanych zagadnień, wyniki przeprowadzonych badań laboratoryjnych i ich analizę oraz wnioski.
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• #### Brief Announcement: Energy Constrained Depth First Search

D. Shantanu, D. Dereniowski, P. Uznański - 2018
Depth first search is a natural algorithmic technique for constructing a closed route that visits all vertices of a graph. The length of such route equals, in an edge-weighted tree, twice the total weight of all edges of the tree and this is asymptotically optimal over all exploration strategies. This paper considers a variant of such search strategies where the length of each route is bounded by a positive integer B (e.g. due...
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• #### Collaborative Exploration of Trees by Energy-Constrained Mobile Robots

S. Das, D. Dereniowski, C. Karousatou - THEORY OF COMPUTING SYSTEMS - 2018
We study the problem of exploration of a tree by mobile agents (robots) that have limited energy. The energy constraint bounds the number of edges that can be traversed by a single agent. We use a team of agents to collectively explore the tree and the objective is to minimize the size of this team. The agents start at a single node, the designated root of the tree and the height of the tree is assumed to be less than the energy...
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• #### Computational aspects of greedy partitioning of graphs

In this paper we consider a variant of graph partitioning consisting in partitioning the vertex set of a graph into the minimum number of sets such that each of them induces a graph in hereditary class of graphs P (the problem is also known as P-coloring). We focus on the computational complexity of several problems related to greedy partitioning. In particular, we show that given a graph G and an integer k deciding if the greedy...
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• #### Connections between Mutually Unbiased Bases and Quantum Random Access Codes

E. Aguilar Lozano, J. Borkała, P. Mironowicz, M. Pawłowski, - PHYSICAL REVIEW LETTERS - 2018
We present a new quantum communication complexity protocol, the promise--Quantum Random Access Code, which allows us to introduce a new measure of unbiasedness for bases of Hilbert spaces. The proposed measure possesses a clear operational meaning and can be used to investigate whether a specific number of mutually unbiased bases exist in a given dimension by employing Semi--Definite Programming techniques.
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• #### Dynamic F-free Coloring of Graphs

P. Borowiecki, E. Sidorowicz - GRAPHS AND COMBINATORICS - 2018
A problem of graph F-free coloring consists in partitioning the vertex set of a graph such that none of the resulting sets induces a graph containing a fixed graph F as an induced subgraph. In this paper we consider dynamic F-free coloring in which, similarly as in online coloring, the graph to be colored is not known in advance; it is gradually revealed to the coloring algorithm that has to color each vertex upon request as well...
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Pokazano, że pewien problem transportu produktów chemicznych może być sprowadzony do problemu szeregowania identycznych zadań kompatybilnych na wsadowych maszynach jednorodnych i rozwiązany metodami kolorowania grafów. Ponieważ problem ten jest NP-trudny, zbadano przypadki szczególne, które dają się rozwiązać w czasie kwadratowym. Rozważania ogólne są wsparte doświadczeniami komputerowymi zebranymi w trakcie implementacji wybranych...
• #### Metody oceny jakości łączy bezprzewodowych wykorzystywanych w systemie netBaltic

Przedstawiono metodę oceny jakości łączy, opracowaną w ramach projektu netBaltic, która powstała w wyniku analizy danych zgromadzonych podczas wielu kampanii pomiarowych na wodach Morza Bałtyckiego oraz badań i testów prowadzonych w środowisku laboratoryjnym. Przedstawiono definicję parametru LQI (Link Quality Indicator) oraz sposób jego wyznaczania dla sieci komórkowych 3G i LTE oraz dla łączy bezprzewodowych WiFi. Zaprezentowano...
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• #### Non-monotone graph searching models

Graph searching encompasses a variety of different models, many of which share a property that in optimal strategies fugitive can never access once searched regions. Monotonicity, as it is called, is vital in many established results in the field however its absence significantly impedes the analysis of a given problem. This survey attempts to gather non-monotone models, that are less researched in effort of summarizing the results...
• #### On incidence coloring of coloring of complete multipartite and semicubic bipartite graphs

In the paper, we show that the incidence chromatic number of a complete k-partite graph is at most ∆+2 (i.e., proving the incidence coloring conjecture for these graphs) and it is equal to ∆+1 if and only if the smallest part has only one vertex.
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• #### On-line Search in Two-Dimensional Environment

We consider the following on-line pursuit-evasion problem. A team of mobile agents called searchers starts at an arbitrary node of an unknown network. Their goal is to execute a search strategy that guarantees capturing a fast and invisible intruder regardless of its movements using as few searchers as possible. As a way of modeling two-dimensional shapes, we restrict our attention to networks that are embedded into partial grids:...
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• #### Oxygen sensitivity of hydrogenesis’ and methanogenesis’

In the chapter, results of dark fermentation of sour cabbage in presence of oxygen with concentrations 2-9% are presented. The presence of oxygen in such concentration inhibits methanogesis (and methane production more than 2 times) and increases hydrogen production 6 times. It also shortens the fermentation process above 40%.
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• #### Scheduling of unit-length jobs with cubic incompatibility graphs on three uniform machines

H. Furmańczyk, M. Kubale - DISCRETE APPLIED MATHEMATICS - 2018
We consider the problem of scheduling n identical jobs on 3 uniform machines with speeds s1, s2, and s3 to minimize the schedule length. We assume that jobs are subject to some kind of mutual exclusion constraints, modeled by a cubic incompatibility graph. We how that if the graph is 2-chromatic then the problem can be solved in O(n^2) time. If the graph is 3-chromatic, the problem becomes NP-hard even if s1>s2=s3.
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• #### Shared processor scheduling

We study the shared processor scheduling problem with a single shared processor to maximize total weighted overlap, where an overlap for a job is the amount of time it is processed on its private and shared processor in parallel. A polynomial-time optimization algorithm has been given for the problem with equal weights in the literature. This paper extends that result by showing an (log)-time optimization algorithm for a class...
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• #### Steering is an essential feature of non-locality in quantum theory

R. Ramanathan, D. Goyeneche, S. Muhammad, P. Mironowicz, M. Grünfeld, M. Bourennane, P. Horodecki - Nature Communications - 2018
A physical theory is called non-local when observers can produce instantaneous effects over distant systems. Non-local theories rely on two fundamental effects: local uncertainty relations and steering of physical states at a distance. In quantum mechanics, the former one dominates the other in a well-known class of non-local games known as XOR games. In particular, optimal quantum strategies for XOR games are completely determined...
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• #### System information propagation for composite structures

We study in details decoherence process of a spin register, coupled to a spin environment. We use recently developed methods of information transfer study in open quantum systems to analyze information flow between the register and its environment. We show that there are regimes when not only the register decoheres effectively to a classical bit string, but this bit string is redundantly encoded in the environment, making it available...
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• #### Tight bounds on the complexity of semi-equitable coloring of cubic and subcubic graphs

H. Furmańczyk, M. Kubale - DISCRETE APPLIED MATHEMATICS - 2018
We consider the complexity of semi-equitable k-coloring, k>3, of the vertices of a cubic or subcubic graph G. In particular, we show that, given a n-vertex subcubic graph G, it is NP-complete to obtain a semi-equitable k-coloring of G whose non-equitable color class is of size s if s>n/3, and it is polynomially solvable if s, n/3.
• #### Trade-offs in multiparty Bell-inequality violations in qubit networks

R. Ramanathan, P. Mironowicz - PHYSICAL REVIEW A - 2018
Two overlapping bipartite binary input Bell inequalities cannot be simultaneously violated as this would contradict the usual no-signalling principle. This property is known as monogamy of Bell inequality violations and generally Bell monogamy relations refer to trade-offs between simultaneous violations of multiple inequalities. It turns out that multipartite Bell inequalities admit weaker forms of monogamies that allow for violations...
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• #### Turán numbers for odd wheels

The Turán number ex(n,G) is the maximum number of edges in any n-vertex graph that does not contain a subgraph isomorphic to G. A wheel W_n is a graph on n vertices obtained from a C_{n−1} by adding one vertex w and making w adjacent to all vertices of the C_{n−1}. We obtain two exact values for small wheels: ex(n,W_5)=\lfloor n^2/4+n/2\rfloor, ex(n,W_7)=\lfloor n^2/4+n/2+1 \rfloor. Given that ex(n,W_6) is already known, this...
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• ### 2017

• #### Approximation Strategies for Generalized Binary Search in Weighted Trees

D. Dereniowski, A. Kosowski, P. Uznański, M. Zou - 2017
We consider the following generalization of the binary search problem. A search strategy is required to locate an unknown target node t in a given tree T. Upon querying a node v of the tree, the strategy receives as a reply an indication of the connected component of T\{v} containing the target t. The cost of querying each node is given by a known non-negative weight function, and the considered objective is to minimize the total...
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• #### Average distance is submultiplicative and subadditive with respect to the strong product of graphs

We show that the average distance is submultiplicative and subadditive on the set of non-trivial connected graphs with respect to the strong product. We also give an application of the above-mentioned result.
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• #### Collaborative Delivery by Energy-Sharing Low-Power Mobile Robots

E. Bampas, S. Das, D. Dereniowski, C. Karousatou - 2017
We study two variants of delivery problems for mobile robots sharing energy. Each mobile robot can store at any given moment at most two units of energy, and whenever two robots are at the same location, they can transfer energy between each other, respecting the maximum capacity. The robots operate in a simple graph and initially each robot has two units of energy. A single edge traversal by an robot reduces its energy by one...
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• #### Collision-free network exploration

J. Czyzowicz, D. Dereniowski, L. Gąsieniec, R. Klasing, A. Kosowski, D. Pająk - JOURNAL OF COMPUTER AND SYSTEM SCIENCES - 2017
Mobile agents start at different nodes of an n-node network. The agents synchronously move along the network edges in a collision-free way, i.e., in no round two agents may occupy the same node. An agent has no knowledge of the number and initial positions of other agents. We are looking for the shortest time required to reach a configuration in which each agent has visited all nodes and returned to its starting location. In...
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• #### Comparing Phylogenetic Trees by Matching Nodes Using the Transfer Distance Between Partitions

D. Bogdanowicz, K. Giaro - JOURNAL OF COMPUTATIONAL BIOLOGY - 2017
Ability to quantify dissimilarity of different phylogenetic trees describing the relationship between the same group of taxa is required in various types of phylogenetic studies. For example, such metrics are used to assess the quality of phylogeny construction methods, to define optimization criteria in supertree building algorithms, or to find horizontal gene transfer (HGT) events. Among the set of metrics described so far in...
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• #### Complementarity between entanglement-assisted and quantum distributed random access code

A. Hameedi, D. Saha, P. Mironowicz, M. Pawłowski, M. Bourennane - PHYSICAL REVIEW A - 2017
Collaborative communication tasks such as random access codes (RACs) employing quantum resources have manifested great potential in enhancing information processing capabilities beyond the classical limitations. The two quantum variants of RACs, namely, quantum random access code (QRAC) and the entanglement-assisted random access code (EARAC), have demonstrated equal prowess for a number of tasks. However, there do exist specific...
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• #### Equitable coloring of corona multiproducts of graphs

H. Furmańczyk, M. Kubale, V. Mkrtchyan - Discussiones Mathematicae Graph Theory - 2017
We give some results regarding the equitable chromatic number for l-corona product of two graphs: G and H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a cycle or a complete graph. Our proofs lead to polynomial algorithms for equitable coloring of such graph products provided that there is given an equitable coloring of G.
• #### Gdańska Międzynarodowa Szkoła Letnia na WETI

M. Kubale - Pismo PG - 2017
W dniach 5-12 września 2017 roku Katedra Algorytmów i Modelowania Systemów23, przy wydatnej pomocy,WETI, zorganizowała Międzynarodową Szkołę Letnią poświęconą algorytmom dla problemów optymalizacji dyskretnej.
• #### Interval incidence coloring of subcubic graphs

In this paper we study the problem of interval incidence coloring of subcubic graphs. In [14] the authors proved that the interval incidence 4-coloring problem is polynomially solvable and the interval incidence 5-coloring problem is N P-complete, and they asked if χii(G) ≤ 2∆(G) holds for an arbitrary graph G. In this paper, we prove that an interval incidence 6-coloring always exists for any subcubic graph G with ∆(G) = 3.
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• #### Monitoring of the Process of System Information Broadcasting in Time

One of the problems of quantum physics is how a measurement turns quantum, noncopyable data, towards copyable classical knowledge. We use the quantum state discrimination in a central system model to show how its evolution leads to the broadcasting of the information, and how orthogonalization and decoherence factors allow us to monitor the distance of the state in question to the one perfectly broadcasting information, in any...
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• #### No-Wait & No-Idle Open Shop Minimum Makespan Scheduling with Bioperational Jobs

In the open shop scheduling with bioperational jobs each job consists of two unit operations with a delay between the end of the first operation and the beginning of the second one. No-wait requirement enforces that the delay between operations is equal to 0. No-idle means that there is no idle time on any machine. We model this problem by the interval incidentor (1, 1)-coloring (IIR(1, 1)-coloring) of a graph with the minimum...
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• #### On Computational Aspects of Greedy Partitioning of Graphs

P. Borowiecki - 2017
In this paper we consider a problem of graph P-coloring consisting in partitioning the vertex set of a graph such that each of the resulting sets induces a graph in a given additive, hereditary class of graphs P. We focus on partitions generated by the greedy algorithm. In particular, we show that given a graph G and an integer k deciding if the greedy algorithm outputs a P-coloring with a least k colors is NP-complete for an infinite...
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• #### Realizacja zadań w grafie przez grupę mobilnych jednostek

D. Osula - 2017
Grupa mobilnych jednostek, nazywanych także agentami, jest umiejscowiona w jednym lub wielu wierzchołkach grafu nazywanych bazami. Stamtąd poruszając się po z góry znanym (offline) lub nieznanym (online) grafie muszą wykonać powierzone im zadanie, takie jak przeszukanie grafu, spotkanie, dekontaminacja grafu czy wybór lidera. Celem jest znalezienie optymalnej, rozproszonej, deterministycznej strategii (sekwencji ruchów jednostek),...
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• #### Restricted open shop scheduling

In the real applications the open shop scheduling models often require some additional constraints and adequate models. We concern the restrictions in the open shop scheduling related to an instance of the problem and to a feasible solution. Precisely, we require that each jobs consists of the bounded number of operations and each machine has a bounded load (i.e., the total number of operations executed on this machine in a schedule)....
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• #### Równowaga strategiczna dla zbiorów defensywnych w drzewach

W pracy rozważany jest problem defensywnej równowagi strategicznej dla zbiorów defensywnych w drzewach (spójnych grafach acyklicznych), który polega na znalezieniu dwóch rozłącznych globalnych zbiorów defensywnych. Zagadnienie to znajduje zastosowanie w modelo- waniu problemów komunikacyjnych w sieciach. Dla danego grafu G podzbiór jego wierzchołków S jest zbiorem defensywnym, jeśli dla każdego wierzchołka v należącego do S spełniony...
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• #### Scheduling of identical jobs with bipartite incompatibility graphs on uniform machines. Computational experiments

We consider the problem of scheduling unit-length jobs on three or four uniform parallel machines to minimize the schedule length or total completion time. We assume that the jobs are subject to some types of mutual exclusion constraints, modeled by a bipartite graph of a bounded degree. The edges of the graph correspond to the pairs of jobs that cannot be processed on the same machine. Although the problem is generally NP-hard,...
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• #### Scheduling of unit-length jobs with bipartite incompatibility graphs on four uniform machines

The problem of scheduling n identical jobs on 4 uniform machines with speeds s1>=s2>=s3>=s4 is considered.The aim is to find a schedule with minimum possible length. We assume that jobs are subject to mutual exclusion constraints modeled by a bipartite incompatibility graph of degree delta. We show that the general problem is NP-hard even if s1=s2=s3. If, however, delta<5 and s1>12s2 s2=s3=s4, then the problem can be solved to...
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• #### Shared multi-processor scheduling

We study shared multi-processor scheduling problem where each job can be executed on its private processor and simultaneously on one of many processors shared by all jobs in order to reduce the job’s completion time due to processing time overlap. The total weighted overlap of all jobs is to be maximized. The problem models subcontracting scheduling in supply chains and divisible load scheduling in computing. We show that synchronized...
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• #### Szeregowanie zadań dwuprocesorowych w systemach otwartych

W pracy rozważany jest problem szeregowania zadań dwuoperacyjnych w systemie otwartym (open-shop), z kryterium minimalizacji długości harmonogramu oraz sumy czasów zakończenia wszystkich zadań. Zakładając jednostkowe czasy wykonywania operacji można stosować efektywne metody chromatyczne rozwiązywania problemu, poprzez sprowadzenie go do modelu grafowego oraz zastosowanie w nim wybranego modelu kolorowania, które pozwala uzyskać...
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• #### Szybkość przeszukiwania grafu

R. Ostrowski - 2017
Przeszukiwanie grafu pojawiło się jako problem matematyczny ponad 40 lat temu i w najogólniejszej wersji zajmuje się odszukiwaniem jednostki-uciekiniera niezależnie od jego poczynań. Od tamtej pory uzyskano wiele wyników odpowiadających na pytanie o minimalną ilość poszukujących jednostek w różnorodnych modelach, czyli odpowiednią liczbę przeszukiwawczą (ang. serach number) grafu. Popularne warianty problemów przeszukiwania obejmują...
• #### The Snow Team Problem

D. Dereniowski, A. Lingas, M. Persson, D. Osula, P. Żyliński - 2017
We study several problems of clearing subgraphs by mobile agents in digraphs. The agents can move only along directed walks of a digraph and, depending on the variant, their initial positions may be pre-specified. In general, for a given subset~$\cS$ of vertices of a digraph $D$ and a positive integer $k$, the objective is to determine whether there is a subgraph $H=(\cV_H,\cA_H)$ of $D$ such that (a) $\cS \subseteq \cV_H$, (b)...
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• ### 2016

• #### An O ( n log n ) algorithm for finding edge span of cacti

Let G=(V,E) be a nonempty graph and xi be a function. In the paper we study the computational complexity of the problem of finding vertex colorings c of G such that: (1) |c(u)-c(v)|>=xi(uv) for each edge uv of E; (2) the edge span of c, i.e. max{|c(u)-c(v)|: uv belongs to E}, is minimal. We show that the problem is NP-hard for subcubic outerplanar graphs of a very simple structure (similar to cycles) and polynomially solvable for...
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• #### Applications of semi-definite optimization in quantum information protocols

P. Mironowicz - 2016
This work is concerned with the issue of applications of the semi-definite programming (SDP) in the field of quantum information sci- ence. Our results of the analysis of certain quantum information protocols using this optimization technique are presented, and an implementation of a relevant numerical tool is introduced. The key method used is NPA discovered by Navascues et al. [Phys. Rev. Lett. 98, 010401 (2007)]. In chapter...
• #### Bounds on the cover time of parallel rotor walks

D. Dereniowski, A. Kosowski, D. Pająk, P. Uznański - JOURNAL OF COMPUTER AND SYSTEM SCIENCES - 2016
The rotor-router mechanism was introduced as a deterministic alternative to the random walk in undirected graphs. In this model, a set of k identical walkers is deployed in parallel, starting from a chosen subset of nodes, and moving around the graph in synchronous steps. During the process, each node successively propagates walkers visiting it along its outgoing arcs in round-robin fashion, according to a fixed ordering. We consider...
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• #### Distributed Evacuation in Graphs with Multiple Exits

We consider the problem of efficient evacuation using multiple exits. We formulate this problem as a discrete problem on graphs where mobile agents located in distinct nodes of a given graph must quickly reach one of multiple possible exit nodes, while avoiding congestion and bottlenecks. Each node of the graph has the capacity of holding at most one agent at each time step. Thus, the agents must choose their movements strategy...
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• #### Edge-coloring of 3-uniform hypergraphs

We consider edge-colorings of 3-uniform hypergraphs which is a natural generalization of the problem of edge-colorings of graphs. Various classes of hypergraphs are discussed and we make some initial steps to establish the border between polynomial and NP-complete cases. Unfortunately, the problem appears to be computationally difficult even for relatively simple classes of hypergraphs.
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• #### Eqiuitable coloring of corona products of cubic graphs is harder than ordinary coloring

A graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the number of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G. In this paper the problem of determinig the equitable coloring number for coronas of cubic graphs is studied. Although the problem of ordinary coloring of coronas...
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• #### Equitable coloring of graphs. Recent theoretical results and new practical algorithms

In this paper we survey recent theoretical results concerning conditions for equitable colorability of some graphs and recent theoretical results concerning the complexity of equitable coloring problem. Next, since the general coloring problem is strongly NP-hard, we report on practical experiments with some efficient polynomial-time algorithms for approximate equitable coloring of general graphs.
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• #### Global defensive sets in graphs

In the paper we study a new problem of finding a minimum global defensive set in a graph which is a generalization of the global alliance problem. For a given graph G and a subset S of a vertex set of G, we define for every subset X of S the predicate SEC ( X ) = true if and only if | N [ X ] ∩ S | ≥ | N [ X ] \ S | holds, where N [ X ] is a closed neighbourhood of X in graph G. A set S is a defensive alliance if and only if for...
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• #### Increased Certification of Semi-device Independent Random Numbers using Many Inputs and More Postprocessing

P. Mironowicz, A. Tavakoli, A. Hameedi, B. Marques, M. Pawłowski, M. Bourennane - NEW JOURNAL OF PHYSICS - 2016
Quantum communication with systems of dimension larger than two provides advantages in information processing tasks. Examples include higher rates of key distribution and random number generation. The main disadvantage of using such multi-dimensional quantum systems is the increased complexity of the experimental setup. Here, we analyze a not-so-obvious problem: the relation between randomness certification and computational requirements...
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• #### Independence in uniform linear triangle-free hypergraphs

P. Borowiecki, M. Gentner, C. Löwenstein, D. Rautenbach - DISCRETE MATHEMATICS - 2016
The independence number a(H) of a hypergraph H is the maximum cardinality of a set of vertices of H that does not contain an edge of H. Generalizing Shearer’s classical lower bound on the independence number of triangle-free graphs Shearer (1991), and considerably improving recent results of Li and Zang (2006) and Chishti et al. (2014), we show a new lower bound for a(H) for an r-uniform linear triangle-free hypergraph H with r>=2.
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• #### Lossless Compression of Binary Trees with Correlated Vertex Names

A. Manager, K. Turowski, W. Szpankowski - 2016
Compression schemes for advanced data structures have become the challenge of today. Information theory has traditionally dealt with conventional data such as text, image, or video. In contrast, most data available today is multitype and context-dependent. To meet this challenge, we have recently initiated a systematic study of advanced data structures such as unlabeled graphs [1]. In this paper, we continue this program by considering...
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• #### Network Graph Transformation Providing Fast Calculation of Paths for Resilient Routing

Protection of transmission against failures can be appropriately dealt with by alternative paths. However, common schemes (e.g., Bhandaris scheme) are characterized by a remarkable delay while determining the transmission paths. This in turn may have a serious impact on serving dynamic demands (characterized by relatively short duration time). As a remedy to this problem, we introduce an approach to pre-compute the sets of disjoint...

A dominating set of a graph $G = (V,E)$ is a set $D$ of vertices of $G$ such that every vertex of $V(G) \setminus D$ has a neighbor in $D$. The domination number of a graph $G$, denoted by $\gamma(G)$, is the minimum cardinality of a dominating set of $G$. The non-isolating bondage number of $G$, denoted by $b'(G)$, is the minimum cardinality among all sets of edges $E' \subseteq E$ such that $\delta(G-E') \ge 1$ and $\gamma(G-E')... • Pełny tekst w serwisie zewnętrznym • #### Normal-form preemption sequences for an open problem in scheduling theory B. Chen, E. Coffman, D. Dereniowski, W. Kubiak - JOURNAL OF SCHEDULING - 2016 Structural properties of optimal preemptive schedules have been studied in a number of recent papers with a primary focus on two structural parameters: the minimum number of preemptions necessary, and a tight lower bound on shifts, i.e., the sizes of intervals bounded by the times created by preemptions, job starts, or completions. These two parameters have been investigated for a large class of preemptive scheduling problems,... • Pełny tekst w serwisie zewnętrznym • #### On bipartization of cubic graphs by removal of an independent set H. Furmańczyk, M. Kubale, S. Radziszowski - DISCRETE APPLIED MATHEMATICS - 2016 We study a new problem for cubic graphs: bipartization of a cubic graph Q by deleting sufficiently large independent set. • Pełny tekst w serwisie zewnętrznym • #### On some open questions for Ramsey and Folkman numbers S. Radziszowski, X. Xiaodong - 2016 We discuss some of our favorite open questions about Ramsey numbers and a related problem on edge Folkman numbers. For the classical two-color Ramsey numbers, we first focus on constructive bounds for the difference between consecutive Ramsey numbers. We present the history of progress on the Ramsey number R(5,5) and discuss the conjecture that it is equal to 43. • #### On the hardness of computing span of subcubic graphs In the paper we study the problem of finding ξ-colorings with minimal span, i.e. the difference between the largest and the smallest color used. • Pełny tekst w serwisie zewnętrznym • #### Sharp bounds for the complexity of semi-equitable coloring of cubic and subcubic graphs M. Kubale, H. Furmańczyk - 2016 In this paper we consider the complexity of semi-equitable k-coloring of the vertices of a cubic or subcubic graph. We show that, given n-vertex subcubic graph G, a semi-equitable k-coloring of G is NP-hard if s >= 7n/20 and polynomially solvable if s <= 7n/21, where s is the size of maximum color class of the coloring. • Pełny tekst w serwisie zewnętrznym • #### Strategic balance in graphs For a given graph G, a nonempty subset S contained in V ( G ) is an alliance iff for each vertex v ∈ S there are at least as many vertices from the closed neighbourhood of v in S as in V ( G ) − S. An alliance is global if it is also a dominating set of G. The alliance partition number of G was defined in Hedetniemi et al. (2004) to be the maximum number of sets in a partition of V ( G ) such that each set is an alliance. Similarly,... • Pełny tekst w serwisie zewnętrznym • #### Szeregowanie identycznych zadań na czterech procesorach jednorodnych z dwudzielnymi grafami konfliktów M. Kubale - 2016 Rozważono problem szeregowania n zadań jednostkowych na 4 procesorach jednorodnych o szybkościach s1>=s2>=s3>=s4. Celem szeregowania jest utworzenie najkrótszego możliwego harmonogramu. Zadania podlegają ograniczeniom zasobowym mówiącym, że niektóre pary zadań nie mogą być wykonane na tym samym procesorze. Podajemy algorytm dokładny, który rozwiązuje problem w czasie liniowym, o ile graf niezgodności jest kubiczny. Ponadto podajemy... • #### Topology recognition and leader election in colored networks Topology recognition and leader election are fundamental tasks in distributed computing in networks. The first of them requires each node to find a labeled isomorphic copy of the network, while the result of the second one consists in a single node adopting the label 1 (leader), with all other nodes adopting the label 0 and learning a path to the leader. We consider both these problems in networks whose nodes are equipped with... • Pełny tekst w serwisie zewnętrznym • ### 2015 • #### 2-outer-independent domination in graphs We initiate the study of 2-outer-independent domination in graphs. A 2-outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of V(G)\D has at least two neighbors in D, and the set V(G)\D is independent. The 2-outer-independent domination number of a graph G is the minimum cardinality of a 2-outer-independent dominating set of G. We show that if a graph has minimum degree at least two,... • Pełny tekst w serwisie zewnętrznym • #### A bound on the number of middle-stage crossbars in f-cast rearrangeable Clos networks In 2006 Chen and Hwang gave a necessary and sufficient condition under which a three-stage Clos network is rearrangeable for broadcast connections. Assuming that only crossbars of the first stage have no fan-out property, we give similar conditions for f-cast Clos networks, where f is an arbitrary but fixed invariant of the network. Such assumptions are valid for some practical switching systems, e.g. high-speed crossconnects.... • #### A Task-Scheduling Approach for Efficient Sparse Symmetric Matrix-Vector Multiplication on a GPU In this paper, a task-scheduling approach to efficiently calculating sparse symmetric matrix-vector products and designed to run on Graphics Processing Units (GPUs) is presented. The main premise is that, for many sparse symmetric matrices occurring in common applications, it is possible to obtain significant reductions in memory usage and improvements in performance when the matrix is prepared in certain ways prior to computation.... • Pełny tekst w serwisie zewnętrznym • #### An upper bound for the double outer-independent domination number of a tree A vertex of a graph is said to dominate itself and all of its neighbors. A double outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D, and the set V(G)\D is independent. The double outer-independent domination number of a graph G, denoted by γ_d^{oi}(G), is the minimum cardinality of a double outer-independent dominating set of G. We prove... • Pełny tekst w serwisie zewnętrznym • #### Bipartite theory of graphs: outer-independent domination Let$G = (V,E)$be a bipartite graph with partite sets$X$and$Y$. Two vertices of$X$are$X$-adjacent if they have a common neighbor in$Y$, and they are$X$-independent otherwise. A subset$D \subseteq X$is an$X$-outer-independent dominating set of$G$if every vertex of$X \setminus D$has an$X$-neighbor in$D$, and all vertices of$X \setminus D$are pairwise$X$-independent. The$X$-outer-independent domination number... • Pełny tekst w serwisie zewnętrznym • #### Deterministic Rendezvous in Restricted Graphs A. Farrugia, L. Gąsieniec, Ł. Kuszner, E. Pacheco - 2015 In this paper we consider the problem of synchronous rendezvous in which two anonymous mobile entities (robots) A and B are expected to meet at the same time and point in a graph G = (V;E). Most of the work devoted to rendezvous in graphs assumes that robots have access to the same sets of nodes and edges, where the topology of connections may be initially known or unknown. In our work we assume the movement of robots is restricted... • Pełny tekst w serwisie zewnętrznym • #### Device-independent quantum key distribution based on measurement inputs R. Rahaman, M. Parker, P. Mironowicz, M. Pawłowski - PHYSICAL REVIEW A - 2015 We provide an analysis of a family of device-independent quantum key distribution (QKD) protocols that has the following features. (a) The bits used for the secret key do not come from the results of the measurements on an entangled state but from the choices of settings. (b) Instead of a single security parameter (a violation of some Bell inequality) a set of them is used to estimate the level of trust in the secrecy of the key.... • Pełny tekst w serwisie zewnętrznym • #### Distinguishing views in symmetric networks: A tight lower bound The view of a node in a port-labeled network is an infinite tree encoding all walks in the network originating from this node. We prove that for any integers n ≥ D ≥ 1, there exists a port-labeled network with at most n nodes and diameter at most D which contains a pair of nodes whose (infinite) views are different, but whose views truncated to depth Omega( D log(n/ D )) are identical. • Pełny tekst w serwisie zewnętrznym • #### Distributed graph searching with a sense of direction In this work we consider the edge searching problem for vertex-weighted graphs with arbitrarily fast and invisible fugitive. The weight function w provides for each vertex v the minimum number of searchers required to guard v, i.e., the fugitive may not pass through v without being detected only if at least w(v) searchers are present at v. This problem is a generalization of the classical edge searching problem, in which one has... • Pełny tekst w serwisie zewnętrznym • #### Equitable and semi-equitable coloring of cubic graphs and its application in batch scheduling In the paper we consider the problems of equitable and semi-equitable coloring of vertices of cubic graphs. We show that in contrast to the equitable coloring, which is easy, the problem of semi-equitable coloring is NP- complete within a broad spectrum of graph parameters. This affects the complexity of batch scheduling of unit-length jobs with cubic incompatibility graph on three uniform processors to minimize... • Pełny tekst w serwisie zewnętrznym • #### Fast collaborative graph exploration D. Dereniowski, Y. Disser, A. Kosowski, D. Pająk, P. Uznański - INFORMATION AND COMPUTATION - 2015 We study the following scenario of online graph exploration. A team of k agents is initially located at a distinguished vertex r of an undirected graph. At every time step, each agent can traverse an edge of the graph. All vertices have unique identifiers, and upon entering a vertex, an agent obtains the list of identifiers of all its neighbors. We ask how many time steps are required to complete exploration, i.e., to make sure... • Pełny tekst w serwisie zewnętrznym • #### Graph security testing Set S ⊂ V is called secure set iff ∀ X ⊂ S | N [ X ] ∩ S | ≥ | N ( X ) \ S | [3]. That means that every subset of a secure set has at least as many friends (neighbour vertices in S) as enemies (neighbour vertices outside S) and will be defended in case of attack. Problem of determining if given set is secure is co −NP -complete, there is no efficient algorithm solving it [3]. Property testers are algorithms that distinguish inputs... • Pełny tekst w serwisie zewnętrznym • #### Interval incidence graph coloring In this paper we introduce a concept of interval incidence coloring of graphs and survey its general properties including lower and upper bounds on the number of colors. Our main focus is to determine the exact value of the interval incidence coloring number χii for selected classes of graphs, i.e. paths, cycles, stars, wheels, fans, necklaces, complete graphs and complete k-partite graphs. We also study the complexity of the... • Pełny tekst w serwisie zewnętrznym • #### KOALA Graph Theory Internet Service KOALA has been created with the idea of C++ library templates, implementing a broad set of procedures in the fields of algorithmic graph theory and network problems in discreate optimization. During the C2NIWA project, a library has been greatly ectended, the code refactored and enclosed with the internet service available in the public repository of thr project. Today it contains interconnected educational materials in the form... • Pełny tekst w serwisie zewnętrznym • #### Minimum order of graphs with given coloring parameters G. Bacsó, P. Borowiecki, M. Hujter, Z. Tuza - DISCRETE MATHEMATICS - 2015 A complete k-coloring of a graph G=(V,E) is an assignment F: V -> {1,...,k} of colors to the vertices such that no two vertices of the same color are adjacent, and the union of any two color classes contains at least one edge. Three extensively investigated graph invariants related to complete colorings are the minimum and maximum number of colors in a complete coloring (chromatic number χ(G) and achromatic number ψ(G), respectively),... • Pełny tekst w serwisie zewnętrznym • #### New potential functions for greedy independence and coloring A potential function$f_G$of a finite, simple and undirected graph$G=(V,E)$is an arbitrary function$f_G : V(G) \rightarrow \mathbb{N}_0$that assigns a nonnegative integer to every vertex of a graph$G$. In this paper we define the iterative process of computing the step potential function$q_G$such that$q_G(v)\leq d_G(v)$for all$v\in V(G)$. We use this function in the development of new Caro-Wei-type and Brooks-type... • Pełny tekst w serwisie zewnętrznym • #### On some Zarankiewicz numbers and bipartite Ramsey Numbers for Quadrilateral J. Dybizbański, T. Dzido, S. Radziszowski - ARS COMBINATORIA - 2015 The Zarankiewicz number z ( m, n ; s, t ) is the maximum number of edges in a subgraph of K m,n that does not contain K s,t as a subgraph. The bipartite Ramsey number b ( n 1 , · · · , n k ) is the least positive integer b such that any coloring of the edges of K b,b with k colors will result in a monochromatic copy of K n i ,n i in the i -th color, for some i , 1 ≤ i ≤ k . If n i = m for all i , then we denote this number by b k ( m ).... • #### On the independence number of some strong products of cycle-powers In the paper we give some theoretical and computational results on the third strong power of cycle-powers, for example, we have found the independence numbers alpha((C^2_10)^⊠3) = 30 and alpha((C^4 _14)^⊠3) = 14. A number of optimizations have been introduced to improve the running time of our exhaustive algorithm used to establish the independence number of the third strong power of cycle-powers. Moreover, our results establish... • Pełny tekst w serwisie zewnętrznym • #### On trees attaining an upper bound on the total domination number A total dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D. The total domination number of a graph G, denoted by γ_t(G), is the minimum cardinality of a total dominating set of G. Chellali and Haynes [Total and paired-domination numbers of a tree, AKCE International Journal of Graphs and Combinatorics 1 (2004), 69-75] established the following upper bound on the total domination... • Pełny tekst w serwisie zewnętrznym • #### On trees with equal 2-domination and 2-outer-independent domination numbers For a graph G = (V,E), a subset D \subseteq V(G) is a 2-dominating set if every vertex of V(G)\D$ has at least two neighbors in D, while it is a 2-outer-independent dominating set if additionally the set V(G)\D is independent. The 2-domination (2-outer-independent domination, respectively) number of G, is the minimum cardinality of a 2-dominating (2-outer-independent dominating, respectively) set of G. We characterize all trees...
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• #### On trees with equal domination and total outer-independent domination numbers

For a graph G=(V,E), a subset D subseteq V(G) is a dominating set if every vertex of V(G)D has a neighbor in D, while it is a total outer-independent dominating set if every vertex of G has a neighbor in D, and the set V(G)D is independent. The domination (total outer-independent domination, respectively) number of G is the minimum cardinality of a dominating (total outer-independent dominating, respectively) set of G. We characterize...
• #### Optimal backbone coloring of split graphs with matching backbones

For a graph G with a given subgraph H, the backbone coloring is defined as the mapping c: V(G) -> N+ such that |c(u)-c(v)| >= 2 for each edge uv \in E(H) and |c(u)-c(v)| >= 1 for each edge uv \in E(G). The backbone chromatic number BBC(G;H) is the smallest integer k such that there exists a backbone coloring with max c(V(G)) = k. In this paper, we present the algorithm for the backbone coloring of split graphs with matching backbone.
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• #### Rendezvous of heterogeneous mobile agents in edge-weighted networks

We introduce a variant of the deterministic rendezvous problem for a pair of heterogeneous agents operating in an undirected graph, which differ in the time they require to traverse particular edges of the graph. Each agent knows the complete topology of the graph and the initial positions of both agents. The agent also knows its own traversal times for all of the edges of the graph, but is unaware of the corresponding traversal...
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• #### Robust amplification of Santha-Vazirani sources with three devices

P. Mironowicz, R. Gallego, M. Pawłowski - PHYSICAL REVIEW A - 2015
We demonstrate that amplification of arbitrarily weak randomness is possible using quantum resources. We present a randomness amplification protocol that involves Bell experiments. We find a Bell inequality which can amplify arbitrarily weak randomness and give a detailed analysis of the protocol involving it. Our analysis includes finding a sufficient violation of Bell inequality as a function of the initial quality of randomness....
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• #### The Backbone Coloring Problem for Bipartite Backbones

Let G be a simple graph, H be its spanning subgraph and λ≥2 be an integer. By a λ -backbone coloring of G with backbone H we mean any function c that assigns positive integers to vertices of G in such a way that |c(u)−c(v)|≥1 for each edge uv∈E(G) and |c(u)−c(v)|≥λ for each edge uv∈E(H) . The λ -backbone chromatic number BBCλ(G,H) is the smallest integer k such that there exists a λ -backbone coloring c of G with backbone H satisfying...
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• #### The complexity of minimum-length path decompositions

We consider a bi-criteria generalization of the pathwidth problem, where, for given integers k, l and a graph G, we ask whether there exists a path decomposition P of G such that the width of P is at most k and the number of bags in P, i.e., the length of P, is at most l. We provide a complete complexity classiﬁcation of the problem in terms of k and l for general graphs. Contrary to the original pathwidth problem, which is ﬁxed-parameter...
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• #### The complexity of zero-visibility cops and robber

D. Dereniowski, D. Dyer, R. Tifenbach, B. Yang - THEORETICAL COMPUTER SCIENCE - 2015
We consider the zero-visibility cops & robber game restricted to trees. We produce a characterisation of trees of copnumber k and We consider the computational complexity of the zero-visibility Cops and Robber game. We present a heavily modified version of an already-existing algorithm that computes the zero-visibility copnumber of a tree in linear time and we show that the corresponding decision problem is NP-complete on a nontrivial...
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• #### The computational complexity of the backbone coloring problem for bounded-degree graphs with connected backbones

Given a graph G, a spanning subgraph H of G and an integer λ>=2, a λ-backbone coloring of G with backbone H is a vertex coloring of G using colors 1, 2, ..., in which the color difference between vertices adjacent in H is greater than or equal to lambda. The backbone coloring problem is to find such a coloring with maximum color that does not exceed a given limit k. In this paper, we study the backbone coloring problem for bounded-degree...
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• #### The computational complexity of the backbone coloring problem for planar graphs with connected backbones

In the paper we study the computational complexity of the backbone coloring problem for planar graphs with connected backbones. For every possible value of integer parameters λ≥2 and k≥1 we show that the following problem: Instance: A simple planar graph GG, its connected spanning subgraph (backbone) HH. Question: Is there a λ-backbone coloring c of G with backbone H such that maxc(V(G))≤k? is either NP-complete or polynomially...
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• #### The searchlight problem for road networks

D. Dereniowski, H. Ono, I. Suzuki, Ł. Wrona, M. Yamashita, P. Żyliński - THEORETICAL COMPUTER SCIENCE - 2015
We consider the problem of searching for a mobile intruder hiding in a road network given as the union of two or more lines, or two or more line segments, in the plane. Some of the intersections of the road network are occupied by stationary guards equipped with a number of searchlights, each of which can emit a single ray of light in any direction along the lines (or line segments) it is on. The goal is to detect the intruder,...
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• #### Towards the boundary between easy and hard control problems in multicast Clos networks

In this article we study 3-stage Clos networks with multicast calls in general and 2-cast calls, in particular. We investigate various sizes of input and output switches and discuss some routing problems involved in blocking states. To express our results in a formal way we introduce a model of hypergraph edge-coloring. A new class of bipartite hypergraphs corresponding to Clos networks is studied. We identify some polynomially...
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• #### Zero-visibility cops and robber and the pathwidth of a graph

D. Dereniowski, D. Dyer, R. Tifenbach, B. Yang - JOURNAL OF COMBINATORIAL OPTIMIZATION - 2015
We examine the zero-visibility cops and robber graph searching model, which differs from the classical cops and robber game in one way: the robber is invisible. We show that this model is not monotonic. We show that the zero-visibility copnumber of a graph is bounded above by its pathwidth and cannot be bounded below by any nontrivial function of the pathwidth. As well, we define a monotonic version of this game and show that the...
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• ### 2014

• #### A survey on known values and bounds on the Shannon capacity

M. Jurkiewicz - 2014
In this survey we present exact values and bounds on the Shannon capacity for different classes of graphs, for example for regular graphs and Kneser graphs. Additionally, we show a relation between Ramsey numbers and Shannon capacity.
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• #### Algorithms for testing security in graphs

In this paper we propose new algorithmic methods giving with the high probability the correct answer to the decision problem of security in graphs. For a given graph G and a subset S of a vertex set of G we have to decide whether S is secure, i.e. every subset X of S fulfils the condition: |N[X] \cap S| >= |N[X] \ S|, where N[X] is a closed neighbourhood of X in graph G. We constructed a polynomial time property pseudotester based...
• #### An algorithm for listing all minimal double dominating sets of a tree

We provide an algorithm for listing all minimal double dominating sets of a tree of order $n$ in time $\mathcal{O}(1.3248^n)$. This implies that every tree has at most $1.3248^n$ minimal double dominating sets. We also show that this bound is tight.
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• #### Bounds on the Cover Time of Parallel Rotor Walks

D. Dereniowski, A. Kosowski, D. Pająk, P. Uznański - 2014
The rotor-router mechanism was introduced as a deterministic alternative to the random walk in undirected graphs. In this model, a set of k identical walkers is deployed in parallel, starting from a chosen subset of nodes, and moving around the graph in synchronous steps. During the process, each node maintains a cyclic ordering of its outgoing arcs, and successively propagates walkers which visit it along its outgoing arcs in...
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• #### Bounds on the vertex-edge domination number of a tree

B. Krishnakumari, Y. Venkatakrishnan, M. Krzywkowski - COMPTES RENDUS MATHEMATIQUE - 2014
A vertex-edge dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every edge of $G$ is incident with a vertex of $D$ or a vertex adjacent to a vertex of $D$. The vertex-edge domination number of a graph $G$, denoted by $\gamma_{ve}(T)$, is the minimum cardinality of a vertex-edge dominating set of $G$. We prove that for every tree $T$ of order $n \ge 3$ with $l$ leaves and $s$ support vertices we have \$(n-l-s+3)/4...
• #### Brushing with additional cleaning restrictions

In graph cleaning problems, brushes clean a graph by traversing it subject to certain rules. We consider the process where at each time step, a vertex that has at least as many brushes as incident, contaminated edges, sends brushes down these edges to clean them. Various problems arise, such as determining the minimum number of brushes (called the brush number) that are required to clean the entire graph. Here, we study a new variant...
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• #### Collision-Free Network Exploration

J. Czyzowicz, D. Dereniowski, L. Gąsieniec, R. Klasing, A. Kosowski, D. Pająk - 2014
A set of mobile agents is placed at different nodes of a n-node network. The agents synchronously move along the network edges in a collision-free way, i.e., in no round may two agents occupy the same node. In each round, an agent may choose to stay at its currently occupied node or to move to one of its neighbors. An agent has no knowledge of the number and initial positions of other agents. We are looking for the shortest possible...
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