Megiddo, Hakimi, Garey, Johnson, and Papadimitriou. The complexity searching graph. the January 1988.  Home/Search Document Not in Database Summary Related Articles Check |
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Straight-Line Drawings on Restricted Integer Grids in.. - Felsner, Liotta, Wismath (2002) (24 citations) (Correct)
....T be a tree. Then pw(T ) max k (T is k strict) pw(T ) 1. Proof. For the proof we compare the strictness of a tree T to its node search number ns(T ) pw(T ) 1 (refer to the beginning of this section for the definitions) In the proof we make use of a lemma attributed to Parsons [32] in [29] [Parsons Lemma] For any tree T and integer k 1, ns(T ) k 1 if and only if T has a vertex v at which there are three or more branches that have search number k or more. First we show that for a tree T k strictness implies ns(T ) k, by induction on k. Assume T is 2 strict. Then T ....
N. Meggido, S. Hakimi, M. Garey, D. Johnson, and C. Papadimitriou. The complexity of searching a graph. JACM 35, 18-44, 1988.
Capture of an Intruder by Mobile Agents - Barrière, Flocchini.. (2002) (2 citations) (Correct)
....of search steps that results in all links being simultaneously clear. The search number s(G) of a network G is the smallest number of searchers for which a search strategy exists. A search strategy using s(G) searchers in G is called minimal. Megiddo, Hakimi, Garey, Johnson and Papadimitriou [24] proved that determining whether s(G) k is NP complete. They gave an O(n) time algorithm to determine the search number of n node trees, and an O(n log n) time algorithm to determine a minimal search strategy in n node trees. Ellis, Sudborough and Turner [9] linked s(G) with the vertex ....
....system while insuring mutual protection and or permanent easy and secure access to the entering point. This motivates the study of edge search where the removal of an agent is not allowed. Even just this assumption considerably changes the nature of the problem. For instance, it is mentioned in [24] that there are trees for which minimal search strategies (i.e. search strategies using the minimum number of searchers) without removal require n log n) moves (i.e. link traversal) whereas, if the removal of agents is allowed, then, for any network G, there exists a minimal search strategy ....
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N. Megiddo, S. Hakimi, M. Garey, D. Johnson and C. Papadimitriou. The complexity of searching a graph. Journal of the ACM 35(1):18-44, 1988.
Locating Information with Uncertainty in Fully.. - Kirousis.. (2000) (1 citation) (Correct)
....not known, have been considered in the past. We have the deterministic search games, where a fugitive that possesses some properties (it is agile or inert) hides in the nodes or edges of a graph and the aim is to locate it using as few searchers as possible (for definitions and relevant theory see [5, 14, 18]) Also, the problem of exploring an unknown graph has been considered (see [2, 19, 20] for example) Closer to the spirit of our work are the search problems that are defined and studied in [4] where the authors consider problems of locating points in the plane using incomplete knowledge about ....
N. Megiddo, S. Hakimi, M. Garey, D. Johnson, and C. Papadimitriou, The complexity of searching a graph, Journal of the ACM 35 (1988), 18--44.
Locating Information with Uncertainty in Fully.. - Kaporis.. (2001) (Correct)
.... characteristics that define the search variant (e.g. it may be moving constantly or it may move only when some searcher is about to visit the node at which it resides) hides in the nodes of the graph and the aim is to capture it using the smallest possible number of searchers (see, for example, [6, 10, 15]) Deterministic algorithms that explore graphs with unknown topology have been studied in [3, 17] There also exists a class of games called stochastic games in which the opponents employ move strategies involving a probability transition matrix (see [20] A description of games that involve ....
N. Megiddo, S. Hakimi, M. Garey, D. Johnson, and C. Papadimitriou (1988) The complexity of searching a graph. Journal of the ACM, 35, 18--44.
Searching with Mobile Agents in Networks with Liars - Hanusse, Kranakis, Krizanc (2002) (Correct)
....the best possible route. Search problems in graphs, where the identity of the node that contains the information sought is not known, have been considered before. These include deterministic search games, where a fugitive that possesses some properties hides in the nodes or edges of a graph [5, 13, 14]) and the problem of exploring an unknown graph [2, 12, 16] Our model is similar in spirit to the model in [4] where the authors propose algorithms to search for a point on a line or on a lattice drawn on the plane. However, in that model, the nodes have limited if any knowledge of where the ....
N. Megiddo, S. Hakimi, M. Garey, D. Johnson, and C. Papadimitriou, The complexity of searching a graph, Journal of the ACM 35 (1988), 18-44.
Computing Small Search Numbers in Linear Time - Bodlaender, Thilikos (1998) (Correct)
....of edge searching and was introduced by Kirousis and Papadimitriou in [14] Finally, mixed searching was introduced in [24] and [2] and is a natural generalisation of the two previous variants (for the formal definitions see Subsection 4. 1 for other results concerning search games on graphs see [1, 7, 9, 15, 16, 23]. The problems of computing es(G) ns(G) ms(G) or linear width(G) is NP complete (see [16, 14, 24, 25] On the other hand, since all of these parameters are closed under taking of minors, we know (see e.g. 3, 19, 20, 22, 21] that, for any k, there exists a linear algorithm that given a ....
....in [24] and [2] and is a natural generalisation of the two previous variants (for the formal definitions see Subsection 4. 1 for other results concerning search games on graphs see [1, 7, 9, 15, 16, 23] The problems of computing es(G) ns(G) ms(G) or linear width(G) is NP complete (see [16, 14, 24, 25]) On the other hand, since all of these parameters are closed under taking of minors, we know (see e.g. 3, 19, 20, 22, 21] that, for any k, there exists a linear algorithm that given a graph G checks whether es(G) ns(G) ms(G) or linear width(G) is at most k (in other words, all these ....
N. Megiddo, S. L. Hakimi, M. R. Garey, D. S. Johnson, and C. H. Papadimitriou. The complexity of searching a graph. J. ACM, 35:18--44, 1988.
Algorithms and Obstructions for Linear-Width and Related Search.. - Thilikos (1997) (1 citation) (Correct)
....by Kirousis and Papadimitriou in [22] Finally, mixed searching was introduced in [35] and [3] and is a natural generalisation of the two previous variants (for the formal definitions see Subsection 5. 1) The problem of computing es(G) ns(G) ms(G) or linear width(G) is NP complete (see [24, 22, 35] and Theorem 5.i of this paper) On the other hand, since all of these parameters is closed under taking of minors, we know that there exist a linear algorithm checking membership in G[f; k] where f is ms, es, ns, or linear width. Such a linear time algorithm has been constructed for the node ....
N. Megiddo, S. L. Hakimi, M. R. Garey, D. S. Johnson, and C. H. Papadimitriou. The complexity of searching a graph. J. ACM, 35:18--44, 1988.
Contiguous and Internal Graph Searching - Barriere, Fraigniaud, Santoro.. (2002) (Correct)
.... 32] and the mixed search number is equal to the proper pathwidth [38, 39] For more on graph searching, we refer the reader to, e.g. 9, 12, 14, 15] Graph searching is a non trivial interesting and challenging problem; even determining whether s(G) k for arbitrary G and k, is NP complete [26]. Not surprisingly, the research has focused on restricted classes of graphs (e.g. 19, 25, 27, 33, 34] and on bounded search numbers (e.g. Departament de Matem atica Aplicada IV, Universitat Polit ecnica de Catalunya, Spain. lali mat.upc.es. CNRS, Laboratoire de Recherche en ....
....after clearing a connected set X of edges, remove the searchers and place them in another part of the graph, usually disconnected from X. The problem of determining minimal search strategies under the contiguity constraint is still NP complete in general (it follows from the reduction in [26], as observed in [1] it has been shown in [1] that minimal contiguous strategies can however be computed in linear time for trees. The next property is perhaps the more practically relevant. A search strategy is internal if, once placed, searchers can only move along the graph edges (i.e. they ....
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N. Megiddo, S. Hakimi, M. Garey, D. Johnson and C. Papadimitriou. The complexity of searching a graph. Journal of the ACM, 35(1):18-44, 1988.
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Megiddo, Hakimi, Garey, Johnson, and Papadimitriou. The complexity searching graph. the January 1988.
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N. Megiddo, S. L. Hakimi, M. R. Garey, D. S. Johnson, and C. H. Papadimitriou. The complexity of searching a graph. J. ACM, 1988.
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N. Megiddo, S. L. Hakimi, M. R. Garey, D. S. Johnson, and C. H. Papadimitriou. The complexity of searching a graph. Journal of the ACM, 35(1):18--44, January 1988.
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N. Megiddo, S. L. Hakimi, M. R. Garey, D. S. Johnson, and C. H. Papadimitriou. The complexity of searching a graph. J. ACM, 1988.
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N. Megiddo, S. Hakimi, M. Garey, D. Johnson and C. Papadimitriou. The complexity of searching a graph. Journal of the ACM 35(1):18--44, 1988.
Straight-Line Drawings on Restricted Integer Grids in.. - Felsner, Liotta, Wismath (2003) (24 citations) (Correct)
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N. Meggido, S. Hakimi, M. Garey, D. Johnson, and C. Papadimitriou. The complexity of searching a graph. JACM 35, 18--44, 1988.
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N. Megiddo, S. L. Hakimi, M. R. Garey, D. S. Johnson, and C. H. Papadimitriou. The complexity of searching a graph. J. Assoc. Comput. Mach., 35(1):18--44, 1988.
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N. Megiddo, S. L. Hakimi, M. R. Garey, D. S. Johnson, and C. H. Papadimitriou. The complexity of searching a graph. J. ACM, 35:18--44, 1988.
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N. Megiddo, S. L. Hakimi, M. R. Garey, D. S. Johnson, and C. H. Papadimitriou. The complexity of searching a graph. J. ACM, 1988.
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N. Megiddo, S. L. Hakimi, M. R. Garey, D. S. Johnson, and C. H. Papadimitriou. On the complexity of searching a graph. J. ACM, 35:18-44, 1988.
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N. Megiddo, S. L. Hakimi, M. R. Garey, D. S. Johnson, and C. H. Papadimitriou. The complexity of searching a graph. J. ACM, 1988.
Connected and Internal Graph Searching - Barriere, Fraigniaud, Santoro.. (Correct)
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N. Megiddo, S. Hakimi, M. Garey, D. Johnson and C. Papadimitriou. The complexity of searching a graph. Journal of the ACM, 35(1):18--44, 1988.
Randomized Pursuit-Evasion with Limited Visibility - Isler, Kannan, Khanna (2004) (Correct)
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N. Megiddo, S. L. Hakimi, M. R. Garey, D. S. Johnson, and C. H. Papadimitriou. The complexity of searching a graph. J. ACM, 1988.
Randomized Pursuit-Evasion with Limited Visibility - Isler, Kannan, Khanna (2004) (Correct)
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N. Megiddo, S. L. Hakimi, M. R. Garey, D. S. Johnson, and C. H. Papadimitriou. The complexity of searching a graph. J. ACM, 1988.
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N. Megiddo, S.L. Hakimi, M. R. Garey, D.S. Johnson, C.H. Papadimitriou, The complexity of searching a graph, J. Assoc. Comput. Mach. 35 (1988), 18-44.
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N. Megiddo, S. L. Hakimi, M. R. Garey, D. S. Johnson, and C. H. Papadimitriou. The complexity of searching a graph. Journal of the ACM, 35(1):18--44, 1988.
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N. Megiddo, S. Hakimi, M. Garey, D. Johnson, and C. Papadimitriou. The complexity of searching a graph. Journal of the ACM, 1988.
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