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Searching for Mobile Intruders in a Polygonal Region by a Group of Mobile Searchers
 SIAM JOURNAL ON COMPUTING
"... The problem of searching for mobile intruders in a polygonal region by mobile searchers is considered. A searcher can move continuously inside a polygon holding a flashlight that emits a single ray of light whose direction can be changed continuously. The visibility of a searcher at any time instant ..."
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Cited by 121 (2 self)
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The problem of searching for mobile intruders in a polygonal region by mobile searchers is considered. A searcher can move continuously inside a polygon holding a flashlight that emits a single ray of light whose direction can be changed continuously. The visibility of a searcher at any time instant is limited to the points on the ray. The intruders can move continuously with unbounded speed. We denote by ps(P ) the polygon search number of a simple polygon P , which is the number of searchers necessary and sufficient to search P . Let n, r, b and g be the number of edges, the number of reflex vertices, the bushiness, and the size of a minimum guard set of P , respectively. In this paper, we present matching upper and (worst case) lower bounds of 1 + blog 3 (2b + 1)c on ps(P ). Also upper bounds on ps(P ) in terms of n; r and g are presented; ps(P ) 1 + blog 3 (n \Gamma 3)c; ps(P ) 1 + blog 3 rc, and ps(P ) 2 + dlog 2 ge. These upper bounds are tight or almost tight in the worst case, since we show that for any natural number s 2, there is a polygon P such that ps(P ) = log 3 (n + 1) = log 3 (2r + 3) = 1 + log 3 (2g \Gamma 1) = s.
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 (25 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...
The Vertex Separation And Search Number Of A Graph
"... We relate two concepts in graph theory and algorithmic complexity, namely the search number and the vertex separation of a graph. Let s (G ) denote the search number and vs (G ) denote the vertex separation of a connected, undirected graph G . We show that vs (G ) s (G ) vs (G ) + 2 and we give a ..."
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Cited by 74 (1 self)
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We relate two concepts in graph theory and algorithmic complexity, namely the search number and the vertex separation of a graph. Let s (G ) denote the search number and vs (G ) denote the vertex separation of a connected, undirected graph G . We show that vs (G ) s (G ) vs (G ) + 2 and we give a simple transformation from G to G such that vs (G ) = s (G ). We characterize those trees having a given vertex separation and describe the smallest such trees. We also note that there exist trees for which the difference between search number and vertex separation is indeed 2. We give algorithms that, for any tree T , compute vs (T ) in linear time and compute an optimal layout with respect to vertex separation in time O (n log n ). Vertex separation has previously been related to progressive black/white pebble demand and has been shown to be identical to a variant of search number, node search number, and to path width, which has been related directly to gate matrix layout cost. All these...
Distributed control applications within sensor networks
 IEEE PROCEEDINGS SPECIAL ISSUE ON DISTRIBUTED SENSOR NETWORKS
, 2003
"... Sensor networks are gaining a central role in the research community. This paper addresses some of the issues arising from the use of sensor networks in control applications. Classical control theory proves to be insufficient in modeling distributed control problems where issues of communication del ..."
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Cited by 71 (24 self)
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Sensor networks are gaining a central role in the research community. This paper addresses some of the issues arising from the use of sensor networks in control applications. Classical control theory proves to be insufficient in modeling distributed control problems where issues of communication delay, jitter, and time synchronization between components are not negligible. After discussing our hardware and software platform and our target application, we review useful models of computation and then suggest a mixed model for design, analysis, and synthesis of control algorithms within sensor networks. We present a hierarchical model composed of continuous timetrigger components at the low level and discrete eventtriggered components at the high level.
Finding an Unpredictable Target in a Workspace with Obstacles
, 1997
"... This paper introduces a visibilitybased motion planning problem in which the task is to coordinate the motions of one or more robots that have omnidirectional vision sensors, to eventually "see" a target that is unpredictable, has unknown initial position, and is capable of moving arbitrarily fast. ..."
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Cited by 65 (14 self)
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This paper introduces a visibilitybased motion planning problem in which the task is to coordinate the motions of one or more robots that have omnidirectional vision sensors, to eventually "see" a target that is unpredictable, has unknown initial position, and is capable of moving arbitrarily fast. A visibility region is associated with each robot, and the goal is to guarantee that the target will ultimately lie in at least one visibility region. Both a formal characterization of the general problem and several interesting problem instances are presented. A complete algorithm for computing the motion strategy of the robots is also presented, and is based on searching a finite cell complex that is constructed on the basis of critical information changes. A few computed solution strategies are shown. Several bounds on the minimum number of needed robots are also discussed. 1 Introduction Have you ever searched for someone in a building, possibly exploring the same places multiple time...
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 64 (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.
Visibilitybased pursuitevasion with limited field of view
 International Journal of Robotics Research
, 2004
"... We study a form of the pursuitevasion problem, in which one or more searchers must move through a given environment so as to guarantee detection of any and all evaders, which can move arbitrarily fast. Our goal is to develop techniques for coordinating teams of robots to execute this task in ap ..."
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Cited by 64 (2 self)
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We study a form of the pursuitevasion problem, in which one or more searchers must move through a given environment so as to guarantee detection of any and all evaders, which can move arbitrarily fast. Our goal is to develop techniques for coordinating teams of robots to execute this task in application domains such as clearing a building, for reasons of security or safety. To this end, we introduce a new class of searcher, the #searcher, which can be readily instantiated as a physical mobile robot. We present a detailed analysis of the pursuitevasion problem using #searchers. We show that computing the minimum number of #searchers required to search a given environment is NPhard, and present the first complete search algorithm for a single #searcher. We show how this algorithm can be extended to handle multiple searchers, and give examples of computed trajectories.
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 51 (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...
VisibilityBased PursuitEvasion in a Polygonal Region by a Searcher
 Proceedings of the International Colloquium on Automata, Languages and Programming (ICALP
, 2001
"... We consider the most basic visibilitybased pursuitevasion problem defined as follows: Given a polygonal region, a searcher with 360 # vision, and an unpredictable intruder that is arbitrarily faster than the searcher, plan the motion of the searcher so as to see the intruder. In this paper, we ..."
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Cited by 43 (1 self)
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We consider the most basic visibilitybased pursuitevasion problem defined as follows: Given a polygonal region, a searcher with 360 # vision, and an unpredictable intruder that is arbitrarily faster than the searcher, plan the motion of the searcher so as to see the intruder. In this paper, we present simple necessary and su#cient conditions for a polygon to be searchable, which settles a decadeold open problem raised in [15]. We also show that every searchable polygon is also searchable by a searcher with two flashlights (that is, ray visions). This implies, combined with the previous work, that there is an O(n 2 )time algorithm for constructing a search path for an nsided polygon. 1 Introduction The visibilitybased pursuitevasion problem is that of planning the motion of one or more searchers in a polygonal environment to eventually see an intruder that is unpredictable, has unknown initial position, and is capable of moving arbitrarily fast. This problem can mode...