Y. Stamatiou and D. Thilikos. Monotonicity and inert fugitive search games. In 6th Twente Workshop on Graphs and Comb. Opt., Elsevier, 1999. Home/Search Document Details and Download
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Capture of an Intruder by Mobile Agents - Barrière, Flocchini.. (2002) (2 citations) (Correct)
....[21] stating that there is a minimal search strategy that does not recontaminate any link (see also [2] Thilikos [36] used graph minors to derive a linear time algorithm that checks whether a network has a search number at most 2. For other results on graph searching, the reader is referred to [7, 8, 12, 30, 32]. Contributions to related search problems can be found in [6, 25, 33, 34, 38, 39] and the references therein. 1.2 Limit of Existing Solutions In all existing solutions for the standard version of the problem (i.e. edge search) as well as for any of its variants known to the authors (e.g. ....
Y. Stamatiou and D. Thilikos. Monotonicity and inert fugitive search games. In 6th Twente Workshop on Graphs and Comb. Opt., Elsevier, 1999.
Connected and Internal Graph Searching - Barriere, Fraigniaud, Santoro.. Self-citation (Thilikos) (Correct)
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Y. Stamatiou and D. Thilikos. Monotonicity and inert fugitive search games. In 6th Twente Workshop on Graphs and Comb. Opt., Elsevier, 1999.
Contiguous and Internal Graph Searching - Barriere, Fraigniaud, Santoro.. (2002) Self-citation (Thilikos) (Correct)
....a singular point in the zoology of search problems. The natural open problem is thus determining the properties of search strategies which are both monotone and internal. Surprisingly, unlike the case of monotone strategies for which there exist detailed studies and characterizations (e.g. [2, 4, 15, 21, 36]) very little is known about contiguous search strategies and monotone internal strategies. Unfortunately, the existing techniques and results for (the many variants of) the problem not only cannot be employed but do not even provide any direct insight on these two important properties. In this ....
Y. Stamatiou and D. Thilikos. Monotonicity and inert fugitive search games. In 6th Twente Workshop on Graphs and Comb. Opt., Elsevier, 1999.
Algorithms and Obstructions for Linear-Width and Related Search.. - Thilikos (2000) (1 citation) Self-citation (Thilikos) (Correct)
....introduced by Kirousis and Papadimitriou in [25] Finally, mixed searching was introduced in [39] and [3] and is a natural generalization of the two previous variants (for the formal definitions see Subsection 5. 1 for analogues versions of the searching game without the agility requirement see [13,36]) The problem of computing es(G) ns(G) ms(G) or linear width(G) is NPcomplete (see [27,25,39] and Theorem 25.i of this paper) On the other hand, since all of these parameters are closed under taking of minors, we know that there exists a linear time algorithm checking membership in G[f; k] ....
....same holds for the parameters of edge search number and mixed search number, defined in the next chapter. Interestingly, this is not the case for other relevant parameters like pathwidth, treewidth, or branchwidth where the obstruction set does not change if we consider multiple edges (see also [36]) 5 Linear width and search parameters In this section we give the definitions of edge searching, node searching, and mixed searching and we prove that the problem of computing the corresponding graph parameters can be reduced to the one of computing linear width. 5.1 Mixed search and other ....
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Y. Stamatiou, D.M. Thilikos, Monotonicity and inert fugitive search games, Report No. LSI-99-35-R, Departament de Llenguatges i Sistemes Inform`atics, Universitat Polyt`ecnica de Catalunya, 1999. http://www.lsi.upc.es/~sedthilk/inert.ps.
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