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58
A Partial KArboretum of Graphs With Bounded Treewidth
 J. Algorithms
, 1998
"... The notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies. This survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class. Also, some mutual relations between such classes ..."
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Cited by 255 (38 self)
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The notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies. This survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class. Also, some mutual relations between such classes are discussed.
Capture of an Intruder by Mobile Agents
, 2002
"... Consider a team of mobile software agents deployed to capture a (possibly hostile) intruder in a network. All agents, including the intruder move along the network links; the intruder could be arbitrarily fast, and aware of the positions of all the agents. The problem is to design the agents' strate ..."
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Cited by 56 (16 self)
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Consider a team of mobile software agents deployed to capture a (possibly hostile) intruder in a network. All agents, including the intruder move along the network links; the intruder could be arbitrarily fast, and aware of the positions of all the agents. The problem is to design the agents' strategy for capturing the intruder. The main eciency parameter is the size of the team. This is an instance of the well known graphsearching problem whose many variants have been extensively studied in the literature. In all existing solutions, and in all the variants of the problem, it is assumed that agents can be removed from their current location and placed in another network site arbitrarily and at any time. As a consequence, the existing optimal strategies cannot be employed in situations for which agents cannot access the network at any point, or cannot "jump" across the network, or cannot reach an arbitrary point of the network via an internal travel through insecure zones. This motivates the contiguous search problem in which agents cannot be removed from the network, and clear links must form a connected subnetwork at any time, providing safety of movements. This new problem is NPcomplete in general. We study it for tree networks, and we consider its more general version, the weighted case, which arises naturally when considering networks whose nodes and links are of different nature and thus require a different number of agents to be explored. We give a lineartime algorithm that computes, for any tree T , the minimum number of agents to capture the intruder, and the corresponding search strategy. Beside its optimality in time, our algorithm is naturally distributed: if T is a processornetwork...
Efficient and Constructive Algorithms for the Pathwidth and Treewidth of Graphs
, 1993
"... In this paper we give, for all constants k, l, explicit algorithms, that given a graph G = (V; E) with a treedecomposition of G with treewidth at most l, decide whether the treewidth (or pathwidth) of G is at most k, and if so, find a treedecomposition or (pathdecomposition) of G of width at most ..."
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Cited by 49 (11 self)
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In this paper we give, for all constants k, l, explicit algorithms, that given a graph G = (V; E) with a treedecomposition of G with treewidth at most l, decide whether the treewidth (or pathwidth) of G is at most k, and if so, find a treedecomposition or (pathdecomposition) of G of width at most k, and that use O(V) time. In contrast with previous solutions, our algorithms do not rely on nonconstructive reasoning, and are single exponential in k and l. This result can be combined with a result of Reed [37], yielding explicit O(n log n) algorithms for the problem, given a graph G, to determine whether the treewidth (or pathwidth) of G is at most k, and if so, to find a tree (or path)decomposition of width at most k (k constant). Also, Bodlaender [13] has used the result of this paper to obtain linear time algorithms for these problems. We also show that for all constants k, there exists a polynomial time algorithm, that, when given a graph G = (V; E) with treewidth k, computes the pathwidth of G and a minimum path decomposition of G.
Randomized PursuitEvasion with Local Visibility
 SIAM Journal on Discrete Mathematics
, 2006
"... We study the following pursuitevasion game: One or more hunters are seeking to capture an evading rabbit on a graph. At each round, the rabbit tries to gather information about the location of the hunters but it can see them only if they are located on adjacent nodes. We show that two hunters su#ce ..."
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Cited by 23 (1 self)
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We study the following pursuitevasion game: One or more hunters are seeking to capture an evading rabbit on a graph. At each round, the rabbit tries to gather information about the location of the hunters but it can see them only if they are located on adjacent nodes. We show that two hunters su#ce for catching rabbits with such local visibility with high probability. We distinguish between reactive rabbits who move only when a hunter is visible and general rabbits who can employ more sophisticated strategies. We present polynomial time algorithms that decide whether a graph G is hunterwin, that is, if a single hunter can capture a rabbit of either kind on G.
Nondeterministic Graph Searching: From Pathwidth to Treewidth
 In 30th International Symposium on Mathematical Foundations of Computer Science (MFCS), LNCS 3618
, 2005
"... Abstract. We introduce nondeterministic graph searching with a controlled amount of nondeterminism and show how this new tool can be used in algorithm design and combinatorial analysis applying to both pathwidth and treewidth. We prove equivalence between this gametheoretic approach and graph decom ..."
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Cited by 17 (6 self)
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Abstract. We introduce nondeterministic graph searching with a controlled amount of nondeterminism and show how this new tool can be used in algorithm design and combinatorial analysis applying to both pathwidth and treewidth. We prove equivalence between this gametheoretic approach and graph decompositions called qbranched tree decompositions, which can be interpreted as a parameterized version of tree decompositions. Path decomposition and (standard) tree decomposition are two extreme cases of qbranched tree decompositions. The equivalence between nondeterministic graph searching and qbranched tree decomposition enables us to design an exact (exponential time) algorithm computing qbranched treewidth for all q ≥ 0, which is thus valid for both treewidth and pathwidth. This algorithm performs as fast as the best known exact algorithm for pathwidth. Conversely, this equivalence also enables us to design a lower bound on the amount of nondeterminism required to search a graph with the minimum number of searchers.
Rerouting requests in wdm networks
 In AlgoTel
, 2005
"... We model a problem related to routing reconfiguration in WDM networks. We establish some similarities and differences with two other known problems: the pathwidth and the pursuit problem. We then present a distributed lineartime algorithm to solve the problem on trees. Last we give the solutions fo ..."
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Cited by 17 (16 self)
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We model a problem related to routing reconfiguration in WDM networks. We establish some similarities and differences with two other known problems: the pathwidth and the pursuit problem. We then present a distributed lineartime algorithm to solve the problem on trees. Last we give the solutions for some classes of graphs, in particular complete dary trees and grids.
Computing Optimal Linear Layouts of Trees in Linear Time
 Proc. ESA 2000, number 1879
, 1999
"... We present a linear time algorithm which, given a tree, computes a linear layout optimal with respect to vertex separation. As a consequence optimal edge search strategies, optimal node search strategies, and optimal interval augmentations can be computed also in O(n) for trees. This improves the ru ..."
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Cited by 14 (0 self)
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We present a linear time algorithm which, given a tree, computes a linear layout optimal with respect to vertex separation. As a consequence optimal edge search strategies, optimal node search strategies, and optimal interval augmentations can be computed also in O(n) for trees. This improves the running time of former algorithms from O(n log n) to O(n) and answers two related open questions raised in [7] and [15].