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Search results for: DIRECTED GRAPH
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A construction for the hat problem on a directed graph
PublicationA 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 space-efficient algorithm for computing the minimum cycle mean in a directed graph
PublicationAn algorithm is introduced for computing the minimum cycle mean in a strongly connected directed graph with n vertices and m arcs that requires O(n) working space. This is a considerable improvement for sparse graphs in comparison to the classical algorithms that require O(n^2) working space. The time complexity of the algorithm is still O(nm). An implementation in C++ is made publicly available at http://www.pawelpilarczyk.com/cymealg/.
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Synchronous black hole search in directed graphs
PublicationThe paper considers a team of robots which has to explore a graph G, where some nodes can be harmful. Robots are initially located at the so-called home base node. The dangerous nodes are the so-called black hole nodes, and once a robot enters in one of them, it is destroyed. The goal is to find a strategy in order to explore G in such a way that minimum number of robots is wasted. The exploration ends if there is at least one...
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Easy and hard instances of arc ranking in directed graphs
PublicationArtykuł dotyczy uporządkowanego kolorowania łuków grafów skierowanych. Problem polega na takim przyporządkowaniu liczb łukom digrafu, aby każda skierowana ścieżka łącząca dwa łuki o tej samej liczbie (kolorze) zawierała łuk o kolorze wyższym. Praca podaje liniowy optymalny algorytm dla pewnego szczególnego przypadku, oraz zawiera dowód, iż problem ten jest obliczeniowo trudny dla 3-dzielnych acyklicznych digrafów i stałej liczby...
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Synchronization helps robots to detect black holes in directed graphs
PublicationPraca zawiera nowe wyniki dla problemu poszukiwania czarnej dziury w grafie skierowanym przez zbiór agentów. Czarna dziura jest węzłem niszczącym wszystkich wchodzącej do niej agentów. Pokazano, że w przypadku, gdy stopień wejściowy czarnej dziury wynosi D, do przeszukania grafu skierowanego w modelu synchronicznym wystarcza O(D 2^D) agentów. Wartość ta jest bliska znanemu z literatury oszacowaniu dolnemu Omega (2^D). W pracy pokazano...
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Clearing directed subgraphs by mobile agents
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 S of vertices of a digraph D and a positive integer k, the objective is to determine whether there is a subgraph H=(V,A) of D such that (a) S is a subset of V, (b) H is the union of k directed...
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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)...
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Network Approach to Increments of RR-intervals for Visualization of Dynamics of Cardiac Regulation
PublicationThe transition network for RR -increments is pre- sented in a directed and weighted graph, with vertices represent- ing RR -increments and edges corresponding to the order in a sequence of increments. The adjacency matrix and the transition matrix of this network provide a graphical tool which could be useful in the assessment of cardiac regulation. As an example, the method is applied in detecting differences between diurnal activity...
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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 maintains a cyclic ordering of its outgoing arcs, and successively propagates walkers which visit it along its outgoing arcs in...
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A model, design, and implementation of an efficient multithreaded workflow execution engine with data streaming, caching, and storage constraints
PublicationThe paper proposes a model, design, and implementation of an efficient multithreaded engine for execution of distributed service-based workflows with data streaming defined on a per task basis. The implementation takes into account capacity constraints of the servers on which services are installed and the workflow data footprint if needed. Furthermore, it also considers storage space of the workflow execution engine and its cost....
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Comparison of selected algorithms for scheduling workflow applications with dynamically changing service availability
PublicationThis paper compares the quality and execution times of several algorithms for scheduling service based workflow applications with changeable service availability and parameters. A workflow is defined as an acyclic directed graph with nodes corresponding to tasks and edges to dependencies between tasks. For each task, one out of several available services needs to be chosen and scheduled to minimize the workflow execution time and...
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KernelHive: a new workflow-based framework for multilevel high performance computing using clusters and workstations with CPUs and GPUs
PublicationThe paper presents a new open-source framework called KernelHive for multilevel parallelization of computations among various clusters, cluster nodes, and finally, among both CPUs and GPUs for a particular application. An application is modeled as an acyclic directed graph with a possibility to run nodes in parallel and automatic expansion of nodes (called node unrolling) depending on the number of computation units available....
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Modele i algorytmy dla grafowych struktur defensywnych
PublicationW niniejszej pracy przeprowadzono analizę złożoności istnienia struktur defensywnych oraz równowag strategicznych w grafach. W przypadku struktur defensywnych badano modele koalicji defensywnych, zbiorów defensywnych i koalicji krawędziowych – każdy z nich w wersji globalnej, tj. z wymogiem dominacji całego grafu. W przypadku modeli równowagi strategicznej badano równowagę strategiczną koalicji defensywnych, równowagę strategiczną...