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Katalog Publikacji
Rok 2015
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On the independence number of some strong products of cycle-powers
PublikacjaIn 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...
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On trees attaining an upper bound on the total domination number
PublikacjaA 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...
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On trees with equal 2-domination and 2-outer-independent domination numbers
PublikacjaFor 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
PublikacjaFor 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...
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Optimal backbone coloring of split graphs with matching backbones
PublikacjaFor 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
PublikacjaWe 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
PublikacjaWe 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
PublikacjaLet 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
PublikacjaWe 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
PublikacjaWe 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
PublikacjaGiven 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
PublikacjaIn 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
PublikacjaWe 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
PublikacjaIn 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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Unicyclic graphs with equal total and total outer-connected domination numbers
PublikacjaLet G = (V,E) be a graph without an isolated vertex. A set D ⊆ V (G) is a total dominating set if D is dominating and the in- duced subgraph G[D] does not contain an isolated vertex. The total domination number of G is the minimum cardinality of a total domi- nating set of G. A set D ⊆ V (G) is a total outer–connected dominating set if D is total dominating and the induced subgraph G[V (G)−D] is a connected graph. The total outer–connected...
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Zero-visibility cops and robber and the pathwidth of a graph
PublikacjaWe 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...
Rok 2014
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A survey on known values and bounds on the Shannon capacity
PublikacjaIn 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
PublikacjaIn 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...
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An algorithm for listing all minimal double dominating sets of a tree
PublikacjaWe 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
PublikacjaThe 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
PublikacjaA 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...
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Brushing with additional cleaning restrictions
PublikacjaIn 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
PublikacjaA 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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Evolution of Animats Following a Moving Target in an Artificial Ecosystem
PublikacjaMany biological animals, even microscopically small, are able to track moving sources of food. In this paper, we investigate the emergence of such behavior in artificial animals (animats) in a 2-dimensional simulated liquid environment. These "predators" are controlled by evolving artificial gene regulatory networks encoded in linear genomes. The fate of the predators is determined only by their ability to gather food and reproduce—no...
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Interval incidence coloring of bipartite graphs
PublikacjaIn this paper we study the problem of interval incidence coloring of bipartite graphs. We show the upper bound for interval incidence coloring number (χii) for bipartite graphs χii≤2Δ, and we prove that χii=2Δ holds for regular bipartite graphs. We solve this problem for subcubic bipartite graphs, i.e. we fully characterize the subcubic graphs that admit 4, 5 or 6 coloring, and we construct a linear time exact algorithm for subcubic...
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Leader election for anonymous asynchronous agents in arbitrary networks
PublikacjaWe consider the problem of leader election among mobile agents operating in an arbitrary network modeled as an undirected graph. Nodes of the network are unlabeled and all agents are identical. Hence the only way to elect a leader among agents is by exploiting asymmetries in their initial positions in the graph. Agents do not know the graph or their positions in it, hence they must gain this knowledge by navigating in the graph...
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Łagodne wprowadzenie do analizy algorytmów
PublikacjaKsiążka jest 11. wydaniem podręcznika akademickiego poświęconego podstawom algorytmiki. Składa się z trzech rozdziałów. Rozdział 1 daje podstawy formalne niezbędne przy analizie algorytmów pod kątem złożoności obliczeniowej. Rozdział 2 wprowadza w zagadnienia analizy algorytmów z różnych punktów widzenia.Rozdział 3 przedstawia podstawowe struktury danych.
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Minimal double dominating sets in trees
PublikacjaWe 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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On practical application of Shannon theory to character recognition and more
PublikacjaLet us consider an optical character recognition system, which in particular can be used for identifying objects that were assigned strings of some length. The system is not perfect, for example, it sometimes recognizes wrongly the characters "Y" and "V". What is the largest set of strings of given length for the system under consideration, which can be mutually correctly recognized, and the corresponding objects correctly identified?...
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Properties of dimension witnesses and their semidefinite programming relaxations
PublikacjaIn this paper we develop a method for investigating semi-device-independent randomness expansion protocols that was introduced in Li et al. [H.-W. Li, P. Mironowicz, M. Pawłowski, Z.-Q. Yin, Y.-C. Wu, S. Wang, W. Chen, H.-G. Hu, G.-C. Guo, and Z.-F. Han, Phys. Rev. A 87, 020302(R) (2013)]. This method allows us to lower bound, with semi-definite programming, the randomness obtained from random number generators based on dimension...
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Rendezvous of Distance-Aware Mobile Agents in Unknown Graphs
PublikacjaWe study the problem of rendezvous of two mobile agents starting at distinct locations in an unknown graph. The agents have distinct labels and walk in synchronous steps. However the graph is unlabelled and the agents have no means of marking the nodes of the graph and cannot communicate with or see each other until they meet at a node. When the graph is very large we want the time to rendezvous to be independent of the graph size...
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Rendezvous of Heterogeneous Mobile Agents in Edge-Weighted Networks
PublikacjaWe 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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Sprawiedliwe i półsprawiedliwe pokolorowania grafów kubicznych
PublikacjaW pracy rozpatrywane są sprawiedliwe i półsprawiedliwe pokolorowania grafów kubicznych. Pokazano, że w odróżnieniu od tego pierwszego, który jest łatwy, problem istnienia pokolorowań półsprawiedliwych jest NP-zupełny w szerokim zakresie parametrów grafów.
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The Backbone Coloring Problem for Small Graphs
PublikacjaIn this paper we investigate the values of the backbone chromatic number, derived from a mathematical model for the problem of minimization of bandwidth in radio networks, for small connected graphs and connected backbones (up to 7 vertices). We study the relationship of this parameter with the structure of the graph and compare the results with the solutions obtained using the classical graph coloring algorithms (LF, IS), modified...
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The Complexity of Zero-Visibility Cops and Robber
PublikacjaIn this work we deal with the computational complexity aspects of the zero-visibility Cops and Robber game. We provide an algorithm that computes the zero-visibility copnumber of a tree in linear time and show that the corresponding decision problem is NP-complete even for the class of starlike graphs.
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Time versus space trade-offs for randezvous in trees
PublikacjaTwo identical (anonymous) mobile agents start from arbitrary nodes of an unknown tree and have to meet at some node. Agents move in synchronous rounds: in each round an agent can either stay at the current node or move to one of its neighbors. We consider deterministic algorithms for this rendezvous task. The main result of this paper is a tight trade-off between the optimal time of completing rendezvous and the size of memory...
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Zgred - Zgred Graph Editor
PublikacjaThe paper presents a graph editor that was developed as a supplementary tool for the Koala graph library. We discuss its requirements, design choices and main ideas behind the implementation. The later part of the paper is meant to be a brief user manual, as we go through the functionality provided by the editor
Rok 2013
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2-bondage in graphs
PublikacjaA 2-dominating set of a graph G=(V,E) is a set D of vertices of G such that every vertex of V(G)D has at least two neighbors in D. The 2-domination number of a graph G, denoted by gamma_2(G), is the minimum cardinality of a 2-dominating set of G. The 2-bondage number of G, denoted by b_2(G), is the minimum cardinality among all sets of edges E' subseteq E such that gamma_2(G-E') > gamma_2(G). If for every E' subseteq E we have...
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An Algorithm for Listing All Minimal 2-Dominating Sets of a Tree
PublikacjaWe provide an algorithm for listing all minimal 2-dominating sets of a tree of order n in time O(1.3248n) . This implies that every tree has at most 1.3248 n minimal 2-dominating sets. We also show that this bound is tigh.
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Certain family of analytical solutions of nonlinear von Neumann equations
PublikacjaIn this paper we present a slight generalization of certain type of Darboux transformation, that may be used sub-sequently in a convenient way. This method allows to obtain families of solutions of nonlinear von Neumann equations, that are used in particular in DNA modeling.
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Deterministic rendezvous of asynchronous bounded-memory agents in polygonal terrains
PublikacjaWe consider two versions of the rendezvous problem: exact RV, when the points representing agents have to coincide at some time, and e-RV, when these points have to get at distance less than e in the terrain. In any terrain, each agent chooses its trajectory, but the movements of the agent on this trajectory are controlled by an adversary that may, e.g. speed up or slow down the agent.
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Drugie Igrzyska Akademii ETI
PublikacjaW sobotę 2 lutego 2013 r. odbyły się drugie Igrzyska Akademii ETI zorganizowane przez Wydział Elektroniki, Telekomunikacji i Informatyki Politechniki Gdańskiej dla uczniów szkół ponadgimnazjalnych regionu. Celem Igrzysk było zwiększenie zainteresowania informatyką młodzieży szkół ponadgimanzjalnych i promocja studiów na Wydziale ETI PG. W tegorocznych Igrzyskach udział wzięli uczniowie z 7 szkół województwa pomorskiego.
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Elementy kwantowego modelu obliczeń i algorytmiki kwantowej : łagodne wprowadzenie do informatyki kwantowej
PublikacjaJuż dziś wiadomo, że z chwilą udanej realizacji komputera kwantowego maszyna ta będzie pozwalała na znajdowanie rozwiązań problemów obliczeniowych leżących poza zasięgiem komputerów klasycznych. Opracowano szereg algorytmów kwantowych, z których największą sławą cieszy się procedura Shora, pozwalająca efektywnie dokonywać tzw. faktoryzacji, tj. rozkładu bardzo dużych liczb naturalnych na czynniki pierwsze. Na trudności obliczeniowej...
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Equitable coloring of corona products of graphs
PublikacjaIn this paper we consider an equitable coloring of some corona products of graphs G and H in symbols, G o H). In particular, we show that deciding the colorability of G o H is NP-complete even if G is 4-regular and H is K_2. Next, we prove exact values or upper bounds on the equitable chromatic number of G o H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a path, a cycle or a complete graph.
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Evolution of artificial single-cell organisms foraging for resources in a 3-dimensional environment
PublikacjaForaging for resources is a simple cognitive task that even one-celled biological organisms can ac- complish. We present an Artificial Life system in which artificial unicellular organisms (animats) forage for food in a 3-dimensional simulated liquid environment. The movement of animats is controlled by evolving artificial gene regulatory networks encoded in linear genomes. When an animat consumes enough food, it produces offspring...
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Evolving gene regulatory networks controlling foraging strategies of prey and predators in an artificial ecosystem
PublikacjaCo-evolution of predators and prey is an example of an evolutionary arms race, leading in nature to selective pressures in positive feedback. We introduce here an artificial life ecosystem in which such positive feedback can emerge. This ecosystem consists of a 2-dimensional liquid environment and animats controlled by evolving artificial gene regulatory networks encoded in linear genomes. The genes in the genome encode chemical...
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Fast Collaborative Graph Exploration
PublikacjaWe 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...
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Minimal 2-dominating sets in Trees
PublikacjaWe provide an algorithm for listing all minimal 2-dominating sets of a tree of order n in time O(1.3247^n). This leads to that every tree has at most 1.3247^n minimal 2-dominating sets. We also show that thisbound is tight.
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Non-isolating 2-bondage in graphs
PublikacjaA 2-dominating set of a graph G=(V,E) is a set D of vertices of G such that every vertex of V(G)D has at least two neighbors in D. The 2-domination number of a graph G, denoted by gamma_2(G), is the minimum cardinality of a 2-dominating set of G. The non-isolating 2-bondage number of G, denoted by b_2'(G), is the minimum cardinality among all sets of edges E' subseteq E such that delta(G-E') >= 1 and gamma_2(G-E') > gamma_2(G)....
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On a matching distance between rooted phylogenetic trees
PublikacjaThe Robinson–Foulds (RF) distance is the most popular method of evaluating the dissimilarity between phylogenetic trees. In this paper, we define and explore in detail properties of the Matching Cluster (MC) distance, which can be regarded as a refinement of the RF metric for rooted trees. Similarly to RF, MC operates on clusters of compared trees, but the distance evaluation is more complex. Using the graph theoretic approach...
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On minimum cost edge searching
PublikacjaWe consider the problem of finding edge search strategies of minimum cost. The cost of a search strategy is the sum of searchers used in the clearing steps of the search. One of the natural questions is whether it is possible to find a search strategy that minimizes both the cost and the number of searchers used to clear a given graph G. We call such a strategy ideal. We prove, by an example, that ideal search strategies do not...
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On the ratio between 2-domination and total outer-independent domination numbers of trees
PublikacjaA 2-dominating set of a graph G is a set D of vertices of G such that every vertex of V(G)D has a at least two neighbors in D. A total outer-independent 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, and the set V(G)D is independent. The 2-domination (total outer-independent domination, respectively) number of a graph G is the minimum cardinality of a 2-dominating (total...
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On trees with double domination number equal to 2-domination number plus one
PublikacjaA vertex of a graph is said to dominate itself and all of its neighbors. A subset D subseteq V(G) is a 2-dominating set of G if every vertex of V(G)D is dominated by at least two vertices of D, while it is a double dominating set of G if every vertex of G is dominated by at least two vertices of D. The 2-domination (double domination, respectively) number of a graph G is the minimum cardinality of a 2-dominating (double dominating,...
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On-line ranking of split graphs
PublikacjaA vertex ranking of a graph G is an assignment of positive integers (colors) to the vertices of G such that each path connecting two vertices of the same color contains a vertex of a higher color. Our main goal is to find a vertex ranking using as few colors as possible. Considering on-line algorithms for vertex ranking of split graphs, we prove that the worst case ratio of the number of colors used by any on-line ranking algorithm...
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Optimal edge-coloring with edge rate constraints
PublikacjaWe consider the problem of covering the edges of a graph by a sequence of matchings subject to the constraint that each edge e appears in at least a given fraction r(e) of the matchings. Although it can be determined in polynomial time whether such a sequence of matchings exists or not [Grötschel et al., Combinatorica (1981), 169–197], we show that several questions about the length of the sequence are computationally intractable....
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Partial dominated schedules and minimizing the total completion time of deteriorating jobs
PublikacjaA problem of scheduling deteriorating jobs on a single processor is considered. The processing time of a job is given by a function pi=ai+bisi, where si is the starting time of the job, ai>=0, bi>=0, for i=1,...,n. Jobs are non-preemptive and independent and there are neither ready times nor deadlines. The goal is to minimize the total weighted completion time. We show how to employ the concept of non-dominated schedules to construct...
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Robustness of quantum-randomness expansion protocols in the presence of noise
PublikacjaIn this paper we investigate properties of several randomness generation protocols in the device independent framework. Using Bell-type inequalities it is possible to certify that the numbers generated by an untrusted device are indeed random. We present a selection of certificates which guarantee two bits of randomness for each run of the experiment in the noiseless case and require the parties to share a maximally entangled state....
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Three-fast-searchable graphs
PublikacjaIn the edge searching problem, searchers move from vertex to vertex in a graph to capture an invisible, fast intruder that may occupy either vertices or edges. Fast searching is a monotonic internal model in which, at every move, a new edge of the graph G must be guaranteed to be free of the intruder. That is, once all searchers are placed the graph G is cleared in exactly |E(G)| moves. Such a restriction obviously necessitates...
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Trees having many minimal dominating sets
PublikacjaWe provide an algorithm for listing all minimal dominating sets of a tree of order n in time O(1.4656^n). This leads to that every tree has at most 1.4656^n minimal dominating sets. We also give an infinite family of trees of odd and even order for which the number of minimal dominating sets exceeds 1.4167^n, thus exceeding 2^{n/2}. This establishes a lower bound on the running time of an algorithm for listing all minimal dominating...
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Zero-Visibility Cops and Robber Game on a Graph
PublikacjaWe examine the zero-visibility cops and robber graph searching model, which differs from the classical cops & robber game in one way: the robber is invisible. We show that this model is not monotonic. We also provide bounds on both the zero-visibility copnumber and monotonic zero-visibility copnumber in terms of the pathwidth.
Rok 2012
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A construction for the hat problem on a directed graph
PublikacjaA team of n players plays the following game. After a strategy session, each player is randomly fitted with a blue or red hat. Then, without further communication, everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. Visibility is defined by a directed graph; that is, vertices correspond to players, and a player can see each player to whom he is connected by an arc. The...
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A lower bound on the double outer-independent domination number of a tree
PublikacjaA 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 gamma_d^{oi}(G), is the minimum cardinality of a double outer-independent dominating set of G. We...
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A Point Set Connection Problem for Autonomous Mobile Robots in a Grid
PublikacjaConsider an orthogonal grid of streets and avenues in a Manhattan-like city populated by stationary sensor modules at some intersections and mobile robots that can serve as relays of information that the modules exchange, where both module-module and module-robot communication is limited to a straight line of sight within the grid. The robots are oblivious and move asynchronously. We present a distributed algorithm that, given...
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An efficient algorithm for finding ideal schedules
PublikacjaPodejmujemy problem szeregowania zadań jednostkowych z zadanymi czasamy przybycia i zależnościami kolejnościowymi. Uszeregowanie jest idealne jeśli jednocześnie minimalizuje maksymalny oraz średni czas zakończenia zadania. Podajemy przyklad pokazujący, że uszeregowania idealne nie istnieją dla relacji zależności zadań będącej drzewem, gdy dopuścimy możliwość wystąpienia przerwań. Z drugiej strony podajemy algorytm o złożoności...
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An upper bound on the total outer-independent domination number of a tree
PublikacjaA total outer-independent dominating set of a graph G=(V(G),E(G)) is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V(G)D is independent. The total outer-independent domination number of a graph G, denoted by gamma_t^{oi}(G), is the minimum cardinality of a total outer-independent dominating set of G. We prove that for every tree T of order n >= 4, with l leaves and s support vertices we have...
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Approximate search strategies for weighted trees
PublikacjaW pracy podajemy 3-przybliżony algorytm dla problemu spójnego przeszukiwania drzew ważonych.
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Colorings of the Strong Product of Circulant Graphs
PublikacjaGraph coloring is one of the famous problems in graph theory and it has many applications to information theory. In the paper we present colorings of the strong product of several circulant graphs.
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Drawing maps with advice
PublikacjaRozważamy następujący problem obliczeniowy. Agent zostaje umieszczony w wierzchołku nieznanego mu grafu. Wierzchołki grafu są nierozróżnialne, natomiast krawędzie posiadają numery portów. Zadaniem agenta jest wyznaczenie mapy, tzn. obliczenie izomorficznej kopii grafu, lub obliczenie dowolnego drzewa spinającego grafu. Bez dodatkowej informacji zadań tych nie można wykonać. W artykule wyznaczamy oszacowania na minimalną liczbę...
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Dynamic coloring of graphs
PublikacjaDynamics is an inherent feature of many real life systems so it is natural to define and investigate the properties of models that reflect their dynamic nature. Dynamic graph colorings can be naturally applied in system modeling, e.g. for scheduling threads of parallel programs, time sharing in wireless networks, session scheduling in high-speed LAN's, channel assignment in WDM optical networks as well as traffic scheduling. In...
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Evolution of chemotaxis in single-cell artificial organisms
PublikacjaThe model of a liquid two-dimensional environment, which is based on physics of diffusion, allows us to simulate the diffusion of morphogenes. Artificial organisms move using a chemotaxis reacting to concentration difference. Organisms are controlled by a gene regulatory network coded in a linear genome and reproduce by division. We made a lot of experiments presenting organisms’ behaviour in various environment conditions. We...
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From Pathwidth to Connected Pathwidth
PublikacjaW pracy przedstawiono dowód faktu, że spójna szerokość ścieżkowa grafu wynosi co najwyżek 2k+1, gdzie k jest jego szerokością ścieżkową. Dowód jest konstruktywny, tzn., został skonstruowany algorytm, który dla podanej na wejściu dekompozycji grafu o szerekości k zwraca dekompozycję spóją o szerekości co najwyżej 2k+1.
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Graph Decomposition for Memoryless Periodic Exploration
PublikacjaWe consider a general framework in which a memoryless robot periodically explores all the nodes of a connected anonymous graph by following local information available at each vertex. For each vertex v, the endpoints of all edges adjacent to v are assigned unique labels within the range 1 to deg (v) (the degree of v). The generic exploration strategy is implemented using a right-hand-rule transition function: after entering vertex...
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Greedy algorithms for backbone graph coloring in KOALA library
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How to meet when you forget: log-space rendezvous in arbitrary graphs
PublikacjaProblem rendezvous został dogłębnie zbadany, zarówno dla agendów anonimowych jak i poetykietowanych. zbadano też problem eksploracji grafu za pomocą agentów mobilnych.
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Igrzyska Akademii ETI : Konkurs dla młodych talentów informatycznych, potencjalnych studentów WETI
PublikacjaSprawozdanie z pierwszych Igrzysk Akademii ETI, które odbyły się 21 stycznia 2012 r.
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Katedra Algorytmów i Modelowania Systemów
PublikacjaPrzedstawiono podstawowe informacje nt. Katedry Algorytmów i Modelowania Systemów Wydziału Elektroniki, Telekomunikacji i Informatyki PG. W szczególności przedstawiono rys historyczny, działalność dydaktyczną, badania podstawowe, nagrody i wyróżnienia oraz ofertę dla przemysłu.
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Kodowanie niedostarczonej do odbiorców informacji w systemach satelitarnych z wolnym kanałem zwrotnym
PublikacjaW poniższym artykule przedstawiono problem kodowania źródła satelitarnego opisany przez Birka i Kola. Przytoczono również nieoptymalne kodowanie dla postawionego problemu oraz miarę określającą możliwości takiego kodowania oraz kilka przykładów, w których wcześniej wspomniane kodowanie staje się optymalne.
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Kolorowanie grafów z ograniczeniami na liczbę wierzchołków w określonym kolorze = Graph coloring model with restrictions on cardinalities of vertexes in particular color
PublikacjaW artykule rozważamy problem takiego kolorowania grafów, w którym klasy kolorów mają ograniczoną z góry moc. Zagadnie to znajduje ciekawe zastosowania praktyczne i jest naturalnym uogólnieniem problemu kolorowania grafów. W artykule ustalamy złożoność obliczeniową dla grafów pełnych $r$-dzielnych i dla kilku innych prostych klas grafów oraz dla problemu dwukolorowania.
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METODA WYZNACZANIA ZŁOŻONOŚCI PODPRZESTRZENI STANÓW PLANSZOWYCH GIER LOGICZNYCH LOGICZNYCH
PublikacjaJedna z metod rozwiązywania gier jest analiza wsteczna. Jej skuteczność jest ograniczona wielkością przestrzeni stanów gry, która stanowi rozwiązywany problem. Pierwszego takiego oszacowania dokonał Claude E. Shannon odnośnie gry szachy w połowie minionego stulecia. Ważnym elementem jest podział takiej przestrzeni na mniejsze części, które mogą być rozwiązywane niezależnie lub z wykorzystaniem stosunkowo niewielkiej ilości informacji z...
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Metody optymalizacji dyskretnej w analizie podobieństwa drzew filognetycznych
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Minimalizacja szerokości pasma w sieciach radiowych metodami szkieletowego kolorowania grafów
PublikacjaArtykuł poświęcony jest szkieletowemu kolorowaniu grafów, które jest matematycznym modelem dla problemu minimalizacji szerokości pasma w sieciach radiowych. Badamy w nim zależność szkieletowej liczby chromatycznej od parametrów zagadnienia. Dowodzimy, że dla dużych wartości parametrów ta zależność jest liniowa.
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Modele i metody kolorowania grafów. Część II
PublikacjaNiniejszy artykuł jest drugą częścią 2-odcinkowego cyklu przeglądowego na temat modeli i metod kolorowania grafów. Przedstawiono w nim najważniejsze, z punktu widzenia zastosowań, modele kolorowania grafów. W szczególności pokazano różne kryteria i ograniczenia modyfikujące kolorowanie klasyczne. Ponieważ kolorowanie we wszystkich tych odmianach i wariantach jest NP-trudne, podano oszacowania na liczbę chromatyczną (indeks chromatyczny)...
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On Optimal Backbone Coloring of Split and Threshold Graphs with Pairwise Disjoint Stars
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On the double bondage in graphs
PublikacjaA vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G=(V,E) is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D. The double domination number of a graph G, denoted by gamma_d(G), is the minimum cardinality of a double dominating set of G. The double bondage number of G, denoted by b_d(G), is the minimum cardinality among all sets...
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On the hat problem on a graph
PublikacjaThe topic of this paper is the hat problem in which each of n players is uniformly and independently fitted with a blue or red hat. Then everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. The team wins if at least one player guesses his hat color correctly, and no one guesses his hat color wrong; otherwise the team loses. The aim is to maximize the probability of winning....
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On the size of identifying codes in triangle-free graphs
PublikacjaIn an undirected graph G, a subset C⊆V(G) such that C is a dominating set of G, and each vertex in V(G) is dominated by a distinct subset of vertices from C, is called an identifying code of G. The concept of identifying codes was introduced by Karpovsky, Chakrabarty and Levitin in 1998. For a given identifiable graph G, let gammaID(G) be the minimum cardinality of an identifying code in G. In this paper, we show that for any connected...
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On trees with double domination number equal to 2-outer-independent domination number plus one
PublikacjaA vertex of a graph is said to dominate itself and all of its neighbors. A double 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. The double domination number of a graph G is the minimum cardinality of a double dominating set of G. 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...
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Product Graph Invariants with Applications in the Theory of Information
PublikacjaThere are a large number of graph invariants. In the paper, we consider some of them, e.g. the independence and chromatic numbers. It is well know that we cannot efficiently calculate these numbers for arbitrary graphs. In the paper we present relations between these invariants and concepts from the theory of information. Concepts such as source coding and transmission over a noisy channel with zero probability of error are modeled...
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Properties of the triset metric for phylogenetic trees
Publikacjathe following paper presents a new polynomial time metric for unrootedphylogenetic trees (based on weighted bipartite graphs and the method ofdetermining a minimum perfect matching) and its properties. also many its properties are presented.
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Routing equal-size messages on a slotted ring
PublikacjaAnalizujemy problem routingu wiadomości w sieci slotted ring, biorąc pod uwagę dwa kryteria optymalizacyjne: długość uszeregowania oraz liczbę 'cykli' pracy sieci. Optymalny routing dla wiadomości o rozmiarze k jest silnie NP-trudny, natomiast dla k=q, gdzie q jest rozmiarem sieci, można obliczyć w czsie O(n^2log n) dla pierwszego kryterium. Podajemy również algorytm o czasie działania O(nlog n) oraz o stałym współczynniku dobroci....
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Some Exact Values of Shannon Capacity for Evolving Systems
PublikacjaWe describe the notion of Shannon Capacity for evolving channels. Furthermore, using a computer search together with some theoretical results we establish some exact values of the measure.
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The Potential of Greed for Independence
PublikacjaThe well-known lower bound on the independence number of a graph due to Caro and Wei can be established as a performance guarantee of two natural and simple greedy algorithms or of a simple randomized algorithm. We study possible generalizations and improvements of these approaches using vertex weights and discuss conditions on so-called potential functions p(G) : V(G) -> N_0 defined on the vertex set of a graph G for which suitably...
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TreeCmp: Comparison of Trees in Polynomial Time
PublikacjaMetryki filogenetyczne umożliwiają ocenę jakości wyników analizy filogenetycznej oraz wiarygodności algorytmów przeprowadzających taką analizę. Aplikacja TreeCmp oferuje efektywne, wielomianowe implementacje ośmiu takich metryk (dla drzew nieukorzenionych i zawierających korzeń) zdefiniowanych dla dowolnych filogenez (nie koniecznie binarnych). Program ten jako pierwszy umożliwia wyznaczanie nowych metryk, definiowanych w oparciu...
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Zastosowanie komputerów w dziedzinie wyszukiwania strategii optymalnych w grach logicznych
PublikacjaProblem jaki stanowi wyszukiwanie strategii optymalnej w grach logicznych jest bardzo złożony. Można go podzielić na następujące podproblemy: obliczeniowy, pamięciowy oraz operacji wejścia/wyjścia. Jednak rosnąca z roku na rok siła obliczeniowa komputerów, ilość pamięci oraz prędkość transferu danych pomiędzy podzespołami zarówno lokalnymi jak i rozproszonymi, a także wzrost skuteczności wykorzystywanych technik algorytmicznych...
Rok 2011
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A lower bound on the total outer-independent domination number of a tree
PublikacjaA total outer-independent 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, and the set V(G)D is independent. The total outer-independent domination number of a graph G, denoted by gamma_t^{oi}(G), is the minimum cardinality of a total outer-independent dominating set of G. We prove that for every nontrivial tree T of order n with l leaves we have gamma_t^{oi}(T) >= (2n-2l+2)/3,...
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A more colorful hat problem
PublikacjaThe topic is the hat problem in which each of n players is randomly fitted with a blue or red hat. Then everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. The team wins if at least one player guesses his hat color correctly, and no one guesses his hat color wrong; otherwise the team loses. The aim is to maximize the probability of winning. We consider a generalized hat...
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A note on fast approximate backbone coloring of split graphs with star--like backbones
PublikacjaDla grafu G = (V, E) z wyróżnionym podgrafem H, kolorowanie szkieletowe jest zdefiniowane jako odwzorowanie c spełniające |c(u) - c(v)| > 1 dla każdej krawędzi z E(H) oraz |c(u) - c(v)| > 0 dla każdej krawędzi z E(G). W pracy przedstawiono 1-przybliżony algorytm kolorowania szkieletowego split grafów ze skojarzeniem w szkielecie o złożoności O(|V|) oraz 1-przybliżony algorytm dla split grafów z rozłącznymi gwiazdami w szkielecie.
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A Note on Shannon Capacity for Invariant and Evolving Channels
PublikacjaIn the paper we discuss the notion of Shannon capacity for invariant and evolving channels. We show how this notion is involved in information theory, graph theory and Ramsey theory.
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An upper bound on the 2-outer-independent domination number of a tree
PublikacjaA 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 a at least two neighbors in D, and the set V(G)D is independent. The 2-outer-independent domination number of a graph G, denoted by gamma_2^{oi}(G), is the minimum cardinality of a 2-outer-independent dominating set of G. We prove that for every nontrivial tree T of order n with l leaves we have gamma_2^{oi}(T) <= (n+l)/2,...
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Analysis of elementary cellular automata using the theory of conflict
PublikacjaThe paper contains decomposition of elementary cellular automata (ECA in short) to subsystems that are defined according to a new theory called theory of conflict (ToC in short). The decomposition is a completely new approach to analysis of ECA and complex systems in general.