Search
Department of Algorithms and Systems Modelling
Publications
Filters
total: 538
Catalog Publications
Year 2018
-
On-line Search in Two-Dimensional Environment
PublicationWe 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:...
-
Oxygen sensitivity of hydrogenesis’ and methanogenesis’
PublicationIn 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%.
-
Pose-Invariant Face Detection by Replacing Deep Neurons with Capsules for Thermal Imagery in Telemedicine
PublicationAbstract— The aim of this work was to examine the potential of thermal imaging as a cost-effective tool for convenient, non- intrusive remote monitoring of elderly people in different possible head orientations, without imposing specific behavior on users, e.g. looking toward the camera. Illumination and pose invariant head tracking is important for many medical applications as it can provide information, e.g. about vital signs, sensory...
-
Programowanie strukturalne
PublicationCelem niniejszej książki jest przedstawienie wybranych metod programowania strukturalnego, tzn. takich, które prowadzą do poprawnej struktury, poprawy jakości oprogramowania oraz zwiększenia efektywności programistów. Może ona służyć jako podręcznik akademicki wykorzystywany na podstawowych kursach inżynierii oprogramowania. Zainteresuje również wszystkich tych, którzy zajmują się programowaniem amatorskim i chcą poszerzyć swoją...
-
Psychotherapy assisted with mobile applications
Publication.
-
Scheduling of unit-length jobs with cubic incompatibility graphs on three uniform machines
PublicationWe 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.
-
Shared processor scheduling
PublicationWe 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...
-
Steering is an essential feature of non-locality in quantum theory
PublicationA 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...
-
System information propagation for composite structures
PublicationWe 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 semi-equitable coloring of cubic and subcubic graphs
PublicationWe 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
PublicationTwo 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...
-
Turán numbers for odd wheels
PublicationThe 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...
Year 2017
-
Approximation Strategies for Generalized Binary Search in Weighted Trees
PublicationWe 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...
-
Average distance is submultiplicative and subadditive with respect to the strong product of graphs
PublicationWe 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.
-
Collaborative Delivery by Energy-Sharing Low-Power Mobile Robots
PublicationWe 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...
-
Collision-free network exploration
PublicationMobile 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...
-
Comparing Phylogenetic Trees by Matching Nodes Using the Transfer Distance Between Partitions
PublicationAbility 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 entanglement-assisted and quantum distributed random access code
PublicationCollaborative 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...
-
Equitable coloring of corona multiproducts of graphs
PublicationWe 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
PublicationW 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
PublicationIn 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.
-
Monitoring of the Process of System Information Broadcasting in Time
PublicationOne 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...
-
No-Wait & No-Idle Open Shop Minimum Makespan Scheduling with Bioperational Jobs
PublicationIn 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...
-
On Computational Aspects of Greedy Partitioning of Graphs
PublicationIn 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...
-
Realizacja zadań w grafie przez grupę mobilnych jednostek
PublicationGrupa 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
PublicationIn 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
PublicationW 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
PublicationWe 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,...
-
Scheduling of unit-length jobs with bipartite incompatibility graphs on four uniform machines
PublicationThe 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...
-
Shared multi-processor scheduling
PublicationWe 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...
-
Szeregowanie zadań dwuprocesorowych w systemach otwartych
PublicationW 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...
-
Szybkość przeszukiwania grafu
PublicationPrzeszukiwanie 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
PublicationWe 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)...
Year 2016
-
An O ( n log n ) algorithm for finding edge span of cacti
PublicationLet 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...
-
Applications of semi-definite optimization in quantum information protocols
PublicationThis 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
PublicationThe 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...
-
Distributed Evacuation in Graphs with Multiple Exits
PublicationWe 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...
-
Edge-coloring of 3-uniform hypergraphs
PublicationWe 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.
-
Eqiuitable coloring of corona products of cubic graphs is harder than ordinary coloring
PublicationA 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...
-
Equitable coloring of graphs. Recent theoretical results and new practical algorithms
PublicationIn 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.
-
Global defensive sets in graphs
PublicationIn 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 Semi-device Independent Random Numbers using Many Inputs and More Postprocessing
PublicationQuantum 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...
-
Independence in uniform linear triangle-free hypergraphs
PublicationThe 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.
-
Lossless Compression of Binary Trees with Correlated Vertex Names
PublicationCompression 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...
-
Network Graph Transformation Providing Fast Calculation of Paths for Resilient Routing
PublicationProtection 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...
-
Non-isolating bondage in graphs
PublicationA 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')...
-
Normal-form preemption sequences for an open problem in scheduling theory
PublicationStructural 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,...
-
On bipartization of cubic graphs by removal of an independent set
PublicationWe study a new problem for cubic graphs: bipartization of a cubic graph Q by deleting sufficiently large independent set.
-
On some open questions for Ramsey and Folkman numbers
PublicationWe 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
PublicationIn 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.