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Search results for: SEARCHING GRAPHS
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A Framework for Searching in Graphs in the Presence of Errors
PublicationWe consider a problem of searching for an unknown target vertex t in a (possibly edge-weighted) graph. Each vertex-query points to a vertex v and the response either admits that v is the target or provides any neighbor s of v that lies on a shortest path from v to t. This model has been introduced for trees by Onak and Parys [FOCS 2006] and for general graphs by Emamjomeh-Zadeh et al. [STOC 2016]. In the latter, the authors provide...
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Distributed graph searching with a sense of direction
PublicationIn this work we consider the edge searching problem for vertex-weighted graphs with arbitrarily fast and invisible fugitive. The weight function w provides for each vertex v the minimum number of searchers required to guard v, i.e., the fugitive may not pass through v without being detected only if at least w(v) searchers are present at v. This problem is a generalization of the classical edge searching problem, in which one has...
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Three-fast-searchable graphs
PublicationIn 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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Application of genetic algorithms in graph searching problem
PublicationGraph searching is a common approach to solving a problem of capturing a hostile intruder by a group of mobile agents. We assume that this task is performed in environment which we are able to model as a graph G. The question asked is how many agents are needed to capture an arbitrary fast, invisible and smart intruder. This number is called the (edge) search number of G. The strategy which must be performed by agents is called...
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Decontaminating Arbitrary Graphs by Mobile Agents: a Survey
PublicationA team of mobile agents starting from homebases need to visit and clean all nodes of the network. The goal is to find a strategy, which would be optimal in the sense of the number of needed entities, the number of moves performed by them or the completion time of the strategy. Currently, the field of distributed graph searching by a team of mobile agents is rapidly expanding and many new approaches and models are being presented...
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Searching by Heterogeneous Agents
PublicationIn this work we introduce and study a pursuit-evasion game in which the search is performed by heterogeneous entities. We incorporate heterogeneity into the classical edge search problem by considering edge-labeled graphs. In such setting a searcher, once a search strategy initially decides on the label of the searcher, can be present on an edge only if the label of the searcher and the label of the edge are the same. We prove...
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The complexity of bicriteria tree-depth
PublicationThe tree-depth problem can be seen as finding an elimination tree of minimum height for a given input graph G. We introduce a bicriteria generalization in which additionally the width of the elimination tree needs to be bounded by some input integer b. We are interested in the case when G is the line graph of a tree, proving that the problem is NP-hard and obtaining a polynomial-time additive 2b-approximation algorithm. This particular...
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On Tradeoffs Between Width- and Fill-like Graph Parameters
PublicationIn this work we consider two two-criteria optimization problems: given an input graph, the goal is to find its interval (or chordal) supergraph that minimizes the number of edges and its clique number simultaneously. For the interval supergraph, the problem can be restated as simultaneous minimization of the path width pw(G) and the profile p(G) of the input graph G. We prove that for an arbitrary graph G and an integer t ∈ {1,...
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On minimum cost edge searching
PublicationWe 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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Searching by heterogeneous agents
PublicationIn this work we introduce and study a pursuit-evasion game in which the search is performed by heterogeneous entities. We incorporate heterogeneity into the classical edge search problem by considering edge-labeled graphs: once a search strategy initially assigns labels to the searchers, each searcher can be only present on an edge of its own label. We prove that this problem is not monotone even for trees and we give instances...
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Modeling and analysis of the effectiveness of the guard systemswith dynamic graphs
PublicationIn the following paper it will be presented a new model for analysis (in polynomial time) of the effectiveness of the guard systems. Therewill be presented its practical applications in problems such as searching for the weakest points of the system, planning guards' paths or cameras deployment, switching image from multiple cameras on several monitors, or interception of the intruder. This model is based on describing the guarded...
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Comparison of reproduction strategies in genetic algorithm approach to graph searching
Publicationgenetic algorithms (ga) are a well-known tool used to obtain approximate solutions to optimization problems. successful application of genetic algorithm in solving given problem is largely dependant on selecting appropriate genetic operators. selection, mutation and crossover techniques play a fundamental role in both time needed to obtain results and their accuracy. in this paper we focus on applying genetic algorithms in calculating...
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Joanna Raczek dr inż.
PeopleEmployment 2003 -- 2019: Faculty of Applied Physics and Mathematics, Gdańsk University of Technology. 2019 - present: Faculty of Electronic, Informatics and Telecominications, Gdańsk University of Technology. Education May 2007: Doctor of Philosophy in Mathematics, University of Gdańsk. Doctoral dissertation: "Paired domination and doubly domination in graphs". Supervisor: dr hab. Jerzy Topp. 2000 -- 2004 Bachelor of Science...
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Non-monotone graph searching models
PublicationGraph searching encompasses a variety of different models, many of which share a property that in optimal strategies fugitive can never access once searched regions. Monotonicity, as it is called, is vital in many established results in the field however its absence significantly impedes the analysis of a given problem. This survey attempts to gather non-monotone models, that are less researched in effort of summarizing the results...