Department of Algorithms and Systems Modelling
Publications
Filters
total: 396
Katalog

2018

ANALIZA MOŻLIWOŚCI WYKORZYSTANIA TRANSFORMACJI FALKOWEJ DO DETEKCJI NIEZAJĘTYCH PASM CZĘSTOTLIWOŚCI
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. 
Brief Announcement: Energy Constrained Depth First Search
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 edgeweighted 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... 
Collaborative Exploration of Trees by EnergyConstrained Mobile Robots
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... 
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 Pcoloring). 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... 
Connections between Mutually Unbiased Bases and Quantum Random Access Codes
We present a new quantum communication complexity protocol, the promiseQuantum 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 SemiDefinite Programming techniques. 
Dynamic Ffree Coloring of Graphs
A problem of graph Ffree 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 Ffree 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... 
Jak transportować produkty chemiczne, czyli przypadek wsadowego szeregowania zadań kompatybilnych
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 NPtrudny, 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... 
Nonmonotone 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 nonmonotone 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 kpartite 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. 
Online Search in TwoDimensional Environment
We consider the following online pursuitevasion 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 twodimensional shapes, we restrict our attention to networks that are embedded into partial grids:... 
Oxygen sensitivity of hydrogenesis’ and methanogenesis’
In the chapter, results of dark fermentation of sour cabbage in presence of oxygen with concentrations 29% 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%. 
Scheduling of unitlength jobs with cubic incompatibility graphs on three uniform machines
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 2chromatic then the problem can be solved in O(n^2) time. If the graph is 3chromatic, the problem becomes NPhard even if s1>s2=s3. 
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 polynomialtime 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... 
Steering is an essential feature of nonlocality in quantum theory
A physical theory is called nonlocal when observers can produce instantaneous effects over distant systems. Nonlocal 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 wellknown class of nonlocal games known as XOR games. In particular, optimal quantum strategies for XOR games are completely determined... 
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... 
Tight bounds on the complexity of semiequitable coloring of cubic and subcubic graphs
We consider the complexity of semiequitable kcoloring, k>3, of the vertices of a cubic or subcubic graph G. In particular, we show that, given a nvertex subcubic graph G, it is NPcomplete to obtain a semiequitable kcoloring of G whose nonequitable color class is of size s if s>n/3, and it is polynomially solvable if s, n/3. 
Tradeoffs in multiparty Bellinequality violations in qubit networks
Two overlapping bipartite binary input Bell inequalities cannot be simultaneously violated as this would contradict the usual nosignalling principle. This property is known as monogamy of Bell inequality violations and generally Bell monogamy relations refer to tradeoffs between simultaneous violations of multiple inequalities. It turns out that multipartite Bell inequalities admit weaker forms of monogamies that allow for violations... 
Turán numbers for odd wheels
The Turán number ex(n,G) is the maximum number of edges in any nvertex 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... 
2017

Approximation Strategies for Generalized Binary Search in Weighted Trees
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 nonnegative weight function, and the considered objective is to minimize the total... 
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 nontrivial connected graphs with respect to the strong product. We also give an application of the abovementioned result. 
Collaborative Delivery by EnergySharing LowPower Mobile Robots
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... 
Collisionfree network exploration
Mobile agents start at different nodes of an nnode network. The agents synchronously move along the network edges in a collisionfree 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... 
Comparing Phylogenetic Trees by Matching Nodes Using the Transfer Distance Between Partitions
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... 
Complementarity between entanglementassisted and quantum distributed random access code
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 entanglementassisted random access code (EARAC), have demonstrated equal prowess for a number of tasks. However, there do exist specific... 
Equitable coloring of corona multiproducts of graphs
We give some results regarding the equitable chromatic number for lcorona product of two graphs: G and H, where G is an equitably 3 or 4colorable graph and H is an rpartite 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
W dniach 512 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 4coloring problem is polynomially solvable and the interval incidence 5coloring problem is N Pcomplete, and they asked if χii(G) ≤ 2∆(G) holds for an arbitrary graph G. In this paper, we prove that an interval incidence 6coloring always exists for any subcubic graph G with ∆(G) = 3. 
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... 
NoWait & NoIdle 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. Nowait requirement enforces that the delay between operations is equal to 0. Noidle 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... 
On Computational Aspects of Greedy Partitioning of Graphs
In this paper we consider a problem of graph Pcoloring 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 Pcoloring with a least k colors is NPcomplete for an infinite... 
Realizacja zadań w grafie przez grupę mobilnych jednostek
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),... 
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).... 
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... 
Scheduling of identical jobs with bipartite incompatibility graphs on uniform machines. Computational experiments
We consider the problem of scheduling unitlength 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 NPhard,... 
Scheduling of unitlength 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 NPhard even if s1=s2=s3. If, however, delta<5 and s1>12s2 s2=s3=s4, then the problem can be solved to... 
Shared multiprocessor scheduling
We study shared multiprocessor 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... 
Szeregowanie zadań dwuprocesorowych w systemach otwartych
W pracy rozważany jest problem szeregowania zadań dwuoperacyjnych w systemie otwartym (openshop), 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... 
Szybkość przeszukiwania grafu
Przeszukiwanie grafu pojawiło się jako problem matematyczny ponad 40 lat temu i w najogólniejszej wersji zajmuje się odszukiwaniem jednostkiuciekiniera 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
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 prespecified. 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)... 
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 NPhard for subcubic outerplanar graphs of a very simple structure (similar to cycles) and polynomially solvable for... 
Applications of semidefinite optimization in quantum information protocols
This work is concerned with the issue of applications of the semidefinite 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
The rotorrouter 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 roundrobin fashion, according to a fixed ordering. We consider... 
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... 
Edgecoloring of 3uniform hypergraphs
We consider edgecolorings of 3uniform hypergraphs which is a natural generalization of the problem of edgecolorings of graphs. Various classes of hypergraphs are discussed and we make some initial steps to establish the border between polynomial and NPcomplete cases. Unfortunately, the problem appears to be computationally difficult even for relatively simple classes of hypergraphs. 
Eqiuitable coloring of corona products of cubic graphs is harder than ordinary coloring
A graph is equitably kcolorable 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... 
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 NPhard, we report on practical experiments with some efficient polynomialtime algorithms for approximate equitable coloring of general graphs. 
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... 
Increased Certification of Semidevice Independent Random Numbers using Many Inputs and More Postprocessing
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 multidimensional quantum systems is the increased complexity of the experimental setup. Here, we analyze a notsoobvious problem: the relation between randomness certification and computational requirements... 
Independence in uniform linear trianglefree hypergraphs
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 trianglefree 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 runiform linear trianglefree hypergraph H with r>=2.