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Theses

Jeux des gendarmes et du voleur dans les graphes. Mineurs de graphes, stratgies connexes, et approche distribue.

Abstract : In graph searching problems, a team of searchers is aiming at catching
a fugitive running in a network. These problems are motivated by
several aspects of theoretical computer science, including
computational complexity and minor graph theory. They have also
numerous practical applications in artificial intelligence and
robotics. In all these contexts, the number of searchers implied in
the capture of the fugitive has a cost and must be minimized. In this
thesis, we study several constraints of search strategie and their
cost in terms of number of searchers. The thesis is divided in three
parts.

In the first part of the thesis, we introduce a new variant of search
strategy that establishs a link between the treewidth and the
pathwidth of a graph. In particular, we prove that this kind of
strategy satisfies the monotonicity property, and we propose a
exponential exact algorithm computing such a strategy.

In the second part of the thesis, we focus on the so-called connected
search strategy that must insure that the clear part of the network
remains permanently connected. We prove several upper and lower bounds
related to the cost of this constraint in terms of number of
searchers. We also study the monotonicity property of the connected
search strategies.

In the third part of the thesis, we study the search strategy in a
decentralized context. We propose several decentralized algorithms
allowing searchers to compute by themselves the strategy that must
be performed.
Document type :
Theses
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https://tel.archives-ouvertes.fr/tel-00168818
Contributor : Nicolas Nisse <>
Submitted on : Thursday, August 30, 2007 - 1:37:52 PM
Last modification on : Wednesday, September 16, 2020 - 4:54:58 PM
Long-term archiving on: : Friday, April 9, 2010 - 1:20:50 AM

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  • HAL Id : tel-00168818, version 1

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Nicolas Nisse. Jeux des gendarmes et du voleur dans les graphes. Mineurs de graphes, stratgies connexes, et approche distribue.. Autre [cs.OH]. Université Paris Sud - Paris XI, 2007. Français. ⟨tel-00168818⟩

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