Contiguous and internal graph searching
Visualitza/Obre
Estadístiques de LA Referencia / Recolecta
Inclou dades d'ús des de 2022
Cita com:
hdl:2117/369736
Tipus de documentReport de recerca
Data publicació2002
Condicions d'accésAccés obert
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Reconeixement-NoComercial-SenseObraDerivada 4.0 Internacional
Abstract
In the graph searching problem, we are given a graph whose edges are all "contaminated", and, via a sequence of "steps" using "searchers", we want to obtain a state of the graph in which all edges are simultaneously "clear". A search strategy is a sequence of search steps that results in all edges being simultaneously clear. The search number s(G) of a graph G is the smallest number of searchers for which a search strategy exists. A search strategy is monotone if no recontamination ever occurs; it is contiguous if the set of clear edges always forms a connected subgraph; and it is internal if searchers, once placed, can only move along the graph edges (i.e., the removal of searchers and their placement somewhere else is not allowed). Depending on the context, each combination of these characteristics may be desirable. Lapaugh proved that, for any graph G, there exists a monotone search strategy for G using s(G) searchers. Obviously, for any graph G there exists an internal search strategy for G using s(G) searchers, but it is not necessarily monotone. We denote by is(G) (resp. cs(G)) the minimum number of searchers for which there exists a monotone internal (resp. contiguous) search strategy in G. We show that, for any graph G, s(G) = is (G) = cs(G) = 2 s(G). Each of these inequalities can be strict. The last inequality is tight. We actually prove the stronger result stating that, for any graph G, there exists a monotone continguous internal search strategy for G using at most 2 s/G) searchers. As a consequence, the contiguous search number cs is a 2-approximation of pathwidth. Finally, we show that there is a unique obstruction for contiguous search and for monotone internal search in trees, in contrast with standard search which involves exponentially many obstructions, even for trees. We prove this result by giving a complete characterization of those searches in trees.
CitacióBarriere, E. [et al.]. Contiguous and internal graph searching. 2002.
Forma partLSI-02-58-R
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