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73
VisibilityBased PursuitEvasion in a Polygonal Environment
 International Journal of Computational Geometry and Applications
, 1997
"... This paper addresses the problem of planning the motion of one or more pursuers in a polygonal environment to eventually "see" an evader that is unpredictable, has unknown initial position, and is capable of moving arbitrarily fast. This problem was first introduced by Suzuki and Yamashita. Our stud ..."
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Cited by 86 (26 self)
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This paper addresses the problem of planning the motion of one or more pursuers in a polygonal environment to eventually "see" an evader that is unpredictable, has unknown initial position, and is capable of moving arbitrarily fast. This problem was first introduced by Suzuki and Yamashita. Our study of this problem is motivated in part by robotics applications, such as surveillance with a mobile robot equipped with a camera that must find a moving target in a cluttered workspace. A few bounds are introduced, and a complete algorithm is presented for computing a successful motion strategy for a single pursuer. For simplyconnected free spaces, it is shown that the minimum number of pursuers required is \Theta(lg n). For multiplyconnected free spaces, the bound is \Theta( p h + lg n) pursuers for a polygon that has n edges and h holes. A set of problems that are solvable by a single pursuer and require a linear number of recontaminations is shown. The complete algorithm searches a f...
A VisibilityBased PursuitEvasion Problem
 SUBMITTED TO THE INTERNATIONAL JOURNAL OF COMPUTATIONAL GEOMETRY AND APPLICATIONS
"... This paper addresses the problem of planning the motion of one or more pursuers in a polygonal environment to eventually "see" an evader that is unpredictable, has unknown initial position, and is capable of moving arbitrarily fast. A visibility region is associated witheach pursuer, and the goal is ..."
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Cited by 65 (1 self)
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This paper addresses the problem of planning the motion of one or more pursuers in a polygonal environment to eventually "see" an evader that is unpredictable, has unknown initial position, and is capable of moving arbitrarily fast. A visibility region is associated witheach pursuer, and the goal is to guarantee that the evader will ultimately lie in at least one visibility region. The study of this problem is motivated inpart by robotics applications, such as surveillance with a mobile robot equipped withacamera that must nd a moving target in a cluttered workspace. A few bounds are introduced, and a complete algorithm is presented for computing a successful motion strategy. For a simplyconnected free space, a logarithmic bound is established on the minimum of pursuers needed. Loose bounds for multiplyconnected free spaces are also given. A set of problems that are solvable by a single pursuer and require a linear number of recontaminations is shown. The complete algorithm searches a nite cell complex that is constructed onthebasis of critical information changes. This concept can be applied in principle to multiplepursuer problems, and the case of a single pursuer has been implemented. Several solution strategies are shown, most of which were computed in a few seconds on a standard workstation.
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...
Eavesdropping games: A graphtheoretic approach to privacy in distributed systems
 JOURNAL OF THE ACM
, 1993
"... We initiate a graphtheoretic approach to study the (informationtheoretic) maintenance of privacy in distributed environments in the presence of a bounded number of mobile eavesdroppers (“bugs”). For two fundamental privacy problems secure message transmission and distributed database maintenanc ..."
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Cited by 37 (2 self)
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We initiate a graphtheoretic approach to study the (informationtheoretic) maintenance of privacy in distributed environments in the presence of a bounded number of mobile eavesdroppers (“bugs”). For two fundamental privacy problems secure message transmission and distributed database maintenance we assume an adversary is “playing eavesdropping games, ” coordinating the movement of the bugs among the sites to learn the current memory contents. We consider various mobility settings (adversaries), motivated by the capabilities (strength) of the bugging technologies (e.g., how fast can a bug be reassigned). We combinatorially characterize and compare privacy maintenance problems, determine their feasibility (under numerous bug models), suggest protocols for the feasible cases, and analyze their computational complexity.
Directed TreeWidth
, 1998
"... We generalize the concept of treewidth to directed graphs, and prove that every directed graph with no "haven" of large order has small treewidth. Conversely, a digraph with a large haven has large treewidth. We also show that the Hamilton cycle problem and other NPhard problems can be solved in ..."
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Cited by 36 (1 self)
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We generalize the concept of treewidth to directed graphs, and prove that every directed graph with no "haven" of large order has small treewidth. Conversely, a digraph with a large haven has large treewidth. We also show that the Hamilton cycle problem and other NPhard problems can be solved in polynomial time when restricted to digraphs of bounded treewidth.
Fugitivesearch games on graphs and related parameters
 THEORETICAL COMPUTER SCIENCE
, 1997
"... ..."
Directed pathwidth and monotonicity in digraph searching
 GRAPHS AND COMBINATORICS
, 2006
"... Directed pathwidth was defined by Reed, Thomas and Seymour around 1995. The author and P. Hajnal defined a copsandrobber game on digraphs in 2000. We prove that the two notions are closely related and for any digraph D, the corresponding graph parameters differ by at most one. The result is achi ..."
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Cited by 19 (0 self)
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Directed pathwidth was defined by Reed, Thomas and Seymour around 1995. The author and P. Hajnal defined a copsandrobber game on digraphs in 2000. We prove that the two notions are closely related and for any digraph D, the corresponding graph parameters differ by at most one. The result is achieved using the mixedsearch technique developed by Bienstock and Seymour. A search is called monotone, in which the robber’s territory never increases. We show that there is a mixedsearch of D with k cops if and only if there is a monotone mixedsearch with k cops. For our copsandrobber game we get a slightly weaker result: the monotonicity can be guaranteed by using at most one extra cop.
Complexity and Security of Distributed Protocols
, 1993
"... This thesis addresses the topic of secure distributed computation, a general and powerful tool for balancing cooperation and mistrust among independent agents. We study many related models, which differ as to the allowable communication among agents, the ways in which agents may misbehave, and the c ..."
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Cited by 19 (0 self)
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This thesis addresses the topic of secure distributed computation, a general and powerful tool for balancing cooperation and mistrust among independent agents. We study many related models, which differ as to the allowable communication among agents, the ways in which agents may misbehave, and the complexity (cryptographic) assumptions that are made. We present new protocols, both for general secure computation (i.e., of any function over a finite domain) and for specific tasks (e.g., electronic money). We investigate fundamental relationships among security needs and various resource requirements, with an emphasis on communication complexity. A number of mathematical methods are employed for our investigations, including algebraic, graphtheoretic, and cryptographic techniques.
GRAPH SEARCHING WITH ADVICE
, 2007
"... Fraigniaud et al. (2006) introduced a new measure of difficulty for a distributed task in a network. The smallest number of bits of advice of a distributed problem is the smallest number of bits of information that has to be available to nodes in order to accomplish the task efficiently. Our paper ..."
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Cited by 18 (7 self)
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Fraigniaud et al. (2006) introduced a new measure of difficulty for a distributed task in a network. The smallest number of bits of advice of a distributed problem is the smallest number of bits of information that has to be available to nodes in order to accomplish the task efficiently. Our paper deals with the number of bits of advice required to perform efficiently the graph searching problem in a distributed setting. In this variant of the problem, all searchers are initially placed at a particular node of the network. The aim of the team of searchers is to capture an invisible and arbitrarily fast fugitive in a monotone connected way, i.e., the cleared part of the graph is permanently connected, and never decreases while the search strategy is executed. We show that the minimum number of bits of advice permitting the monotone connected clearing of a network in a distributed setting is O(n log n), where n is the number of nodes of the network, and this bound is tight. More precisely, we first provide a labelling of the vertices of any graph G, using a total of O(n log n) bits, and a protocol using this labelling that enables clearing G in a monotone connected distributed way. Then, we show that this number of bits of advice is almost optimal: no protocol using an oracle providing o(n log n) bits of advice permits the monotone connected clearing of a network using the smallest number of searchers.