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.

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 multiply-connected 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...

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...

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This paper introduces a visibility-based 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...

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 simply-connected free space, a logarithmic bound is established on the minimum of pursuers needed. Loose bounds for multiply-connected 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 multiple-pursuer 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.

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 time-trigger components at the low level and discrete event-triggered components at the high level. Keywords—Distributed control, distributed pursuit–evasion game (DPEG), embedded, Mica, mote, NesC, pursuit–evasion game (PEG), sensor network, TinyOS. I.

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 graph-searching 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 sub-network at any time, providing safety of movements. This new problem is NP-complete 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 linear-time 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 processor-network...

We initiate a graph-theoretic approach to study the (information-theoretic) maintenance of privacy in dis-tributed environments in the presence of a bounded number of mobile eavesdroppers (“bugs”). For two fundamental privacy problems- secure message trans-mission and distributed database maintenance- we as-sume 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 combi-natorially characterize and compare privacy mainte-nance problems, determine their feasibility (under nu-merous bug models), suggest protocols for the feasible cases, and analyze their computational complexity.

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