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Faulttolerant gathering algorithms for autonomous mobile robots
 SIAM J. Comput
, 2004
"... This paper studies fault tolerant algorithms for the problem of gathering N autonomous mobile robots. A gathering algorithm, executed independently by each robot, must ensure that all robots are gathered at one point within nite time. In a failureprone system, a gathering algorithm is required to ..."
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Cited by 52 (4 self)
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This paper studies fault tolerant algorithms for the problem of gathering N autonomous mobile robots. A gathering algorithm, executed independently by each robot, must ensure that all robots are gathered at one point within nite time. In a failureprone system, a gathering algorithm is required to successfully gather the nonfaulty robots, independently of the behavior of the faulty ones. Both crash and Byzantine faults are considered. It is rst observed that most existing algorithms fail to operate correctly in a setting allowing crash failures. Subsequently, an algorithm tolerant against one crashfaulty robot in a system of three or more robots is presented. It is then observed that all known algorithms fail to operate correctly in a system prone to Byzantine faults, even in the presence of a single fault. Moreover, it is shown that in an asynchronous environment it is impossible to perform a successful gathering in a 3robot system, even if at most one of them might fail in a Byzantine manner. Thus, the problem is studied in a fully synchronous system. An algorithm is provided in this model for gathering N 3 robots with at most a single faulty robot, and a more general gathering algorithm is given in an Nrobot system with up to f faults, where N 3f +1.
Collective Tree Exploration
 In: Proc. LATIN 2004. Volume
, 2004
"... An nnode tree has to be explored by k mobile agents (robots), starting in its root. Every edge of the tree must be traversed by at least one robot, and exploration must be completed as fast as possible. Even when the tree is known in advance, scheduling optimal collective exploration turns out t ..."
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Cited by 29 (5 self)
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An nnode tree has to be explored by k mobile agents (robots), starting in its root. Every edge of the tree must be traversed by at least one robot, and exploration must be completed as fast as possible. Even when the tree is known in advance, scheduling optimal collective exploration turns out to be NPhard. We investigate the problem of distributed collective exploration of unknown trees.
Mobile Search for a Black Hole in an Anonymous Ring
"... We address the problem of mobile agents searching a ring network for a highly harmful item, a black hole, a stationary process destroying visiting agents upon their arrival. No observable trace of such a destruction will be evident. The location of the black hole is not known; the task is to una ..."
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Cited by 18 (11 self)
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We address the problem of mobile agents searching a ring network for a highly harmful item, a black hole, a stationary process destroying visiting agents upon their arrival. No observable trace of such a destruction will be evident. The location of the black hole is not known; the task is to unambiguously determine and report the location of the black hole. We answer some natural computational questions: How many agents are needed to locate the black hole in the ring ? How many suce? What apriori knowledge is required? as well as complexity questions, such as: With how many moves can the agents do it ? How long does it take ? Keywords: Mobile Agents, Distributed Computing, Ring Network, Hazardous Search.
Convergence of Autonomous Mobile Robots with Inaccurate Sensors and Movements
 In Proc. 23 th Annual Symposium on Theoretical Aspects of Computer Science (STACS ’06
, 2006
"... Anumber of recent studies concern algorithms for distributed control and coordination in systems of autonomous mobile robots. The common theoretical model adopted in these studies assumes that the positional input of the robots is obtained by perfectly accurate visual sensors, that robot movements a ..."
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Cited by 18 (1 self)
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Anumber of recent studies concern algorithms for distributed control and coordination in systems of autonomous mobile robots. The common theoretical model adopted in these studies assumes that the positional input of the robots is obtained by perfectly accurate visual sensors, that robot movements are accurate, and that internal calculations performed by the robots on (real) coordinates are perfectly accurate as well. The current paper concentrates on the e ect of weakening this rather strong set of assumptions, and replacing it with the more realistic assumption that the robot sensors, movement and internal calculations may have slight inaccuracies. Speci cally, the paper concentrates on the ability of robot systems with inaccurate sensors, movements and calculations to carry out the task of convergence. The paper presents several impossibility theorems, limiting the inaccuracy allowing convergence, and prohibiting a general algorithm for gathering, namely, meeting at a point, in a nite number of steps. The main positive result is an algorithm for convergence under bounded measurement, movement and calculation errors.
Multiple agents rendezvous in a ring in spite of a black hole
 In Proc. Symposium on Principles of Distributed Systems (OPODIS ’03), volume 3144 of LNCS
, 2003
"... The Rendezvous of anonymous mobile agents in a anonymous network is an intensively studied problem; it calls for k anonymous, mobile agents to gather in the same site. We study this problem when in the network there is a black hole: a stationary process located at a node that destroys any incoming a ..."
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Cited by 16 (6 self)
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The Rendezvous of anonymous mobile agents in a anonymous network is an intensively studied problem; it calls for k anonymous, mobile agents to gather in the same site. We study this problem when in the network there is a black hole: a stationary process located at a node that destroys any incoming agent without leaving any trace. The presence of the black hole makes it clearly impossible for all agents to rendezvous. So, the research concern is to determine how many agents can gather and under what conditions. In this paper we consider k anonymous, asynchronous mobile agents in an anonymous ring of size n with a black hole; the agents are aware of the existence, but not of the location of such a danger. We study the rendezvous problem in this setting and establish a complete characterization of the conditions under which the problem can be solved. In particular, we determine the maximum number of agents that can be guaranteed to gather in the same location depending on whether k or n is unknown (at least one must be known for any nontrivial rendezvous). These results are tight: in each case, rendezvous with one more agent is impossible. All our possibility proofs are constructive: we provide mobile agents protocols that allow the agents to rendezvous or neargather under the specified conditions. The analysis of the time costs of these protocols show that they are optimal. Our rendezvous protocol for the case when k is unknown is also a solution for the black hole location problem. Interestingly, its bounded time complexity is Θ(n); this is a significant improvement over the O(n log n) bounded time complexity of the existing protocols for the same case.
Minimizing Movement
"... We give approximation algorithms and inapproximability results for a class of movement problems. In general, these problems involve planning the coordinated motion of a large collection of objects (representing anything from a robot swarm or firefighter team to map labels or network messages) to ach ..."
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Cited by 14 (2 self)
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We give approximation algorithms and inapproximability results for a class of movement problems. In general, these problems involve planning the coordinated motion of a large collection of objects (representing anything from a robot swarm or firefighter team to map labels or network messages) to achieve a global property of the network while minimizing the maximum or average movement. In particular, we consider the goals of achieving connectivity (undirected and directed), achieving connectivity between a given pair of vertices, achieving independence (a dispersion problem), and achieving a perfect matching (with applications to multicasting). This general family of movement problems encompass an intriguing range of graph and geometric algorithms, with several realworld applications and a surprising range of approximability. In some cases, we obtain tight approximation and inapproximability results using direct techniques (without use of PCP), assuming just that P != NP.
Improved approximation algorithms for the freezetag problem
 In Proceedings of the 15th annual ACM symposium on Parallel algorithms and architectures
, 2003
"... Abstract The following scheduling problem naturally arises in thestudy of swarm robotics. Consider a set of n robots, modeled as points in some metric space (e.g., vertices of an edgeweighted graph). Initially, there is one awake oractive robot and all other robots are asleep, that is, in a stand ..."
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Cited by 12 (1 self)
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Abstract The following scheduling problem naturally arises in thestudy of swarm robotics. Consider a set of n robots, modeled as points in some metric space (e.g., vertices of an edgeweighted graph). Initially, there is one awake oractive robot and all other robots are asleep, that is, in a standby mode. Our objective is to "wake up " all ofthe robots as quickly as possible. In order for an active robot to awaken a sleeping robot, the awake robotmust travel to the location of the slumbering robot. Once awake, this new robot is available to assist in rousing otherrobots. The objective is to minimize the makespan, that is, the time when the last robot awakens. This problemis the FreezeTag Problem (FTP) because it resembles the child's game of freezetag. The FTP is a scheduling problem that arises naturallyas a hybrid of problems from the areas of broadcasting,
Approximating the degreebounded minimum diameter spanning tree problem
 ALGORITHMICA
, 2003
"... We consider the problem of finding a minimum diameter spanning tree with maximum node degree B in a complete undirected edgeweighted graph. We provide an O ( p log B n)approximation algorithm for the problem. Our algorithm is purely combinatorial, and relies on a combination of filtering and divi ..."
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Cited by 12 (0 self)
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We consider the problem of finding a minimum diameter spanning tree with maximum node degree B in a complete undirected edgeweighted graph. We provide an O ( p log B n)approximation algorithm for the problem. Our algorithm is purely combinatorial, and relies on a combination of filtering and divide and conquer.
Analysis of Heuristics for the FreezeTag Problem
 In Proc. Scandinavian Workshop on Algorithms, Vol. 2368 of SpringerVerlag LNCS
, 2002
"... In the Freeze Tag Problem (FTP) we are given a swarm of n asleep (frozen or inactive) robots and a single awake (active) robot, and we want to awaken all robots in the shortest possible time. A robot is awakened when an active robot "touches" it. The goal is to compute an optimal awakening schedule ..."
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Cited by 11 (3 self)
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In the Freeze Tag Problem (FTP) we are given a swarm of n asleep (frozen or inactive) robots and a single awake (active) robot, and we want to awaken all robots in the shortest possible time. A robot is awakened when an active robot "touches" it. The goal is to compute an optimal awakening schedule such that all robots are awake by time t , for the smallest possible value of t . We devise and test a variety of heuristic strategies on geometric and network datasets. Our experiments show that all of the strategies perform well, with the simple greedy strategy performing particularly well. A theoretical analysis of the greedy strategy gives a tight approximation bound of ( log n) for points in the plane. We show more generally that the (tight) performance bound is ((log n) ) in d dimensions. This is in contrast with the case of general metric spaces, where greedy is known to have a (log n) approximation factor, and no method is known to achieve an approximation bound of o(log n).
Improved bounds for optimal black hole search in a network with a map
 In Proc. of 10th International Colloquium on Structural Information and Communication Complexity
, 2004
"... Abstract. A black hole is a harmful host that destroys incoming agents without leaving any observable trace of such a destruction. The black hole search problem is to unambiguously determine the location of the black hole. A team of agents, provided with a network map and executing the same protocol ..."
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Cited by 7 (6 self)
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Abstract. A black hole is a harmful host that destroys incoming agents without leaving any observable trace of such a destruction. The black hole search problem is to unambiguously determine the location of the black hole. A team of agents, provided with a network map and executing the same protocol, solves the problem if at least one agent survives and, within finite time, knows the location of the black hole. It is known that a team must have at least two agents. Interestingly, two agents with a map of the network can locate the black hole with O(n) moves in many highly regular networks; however the protocols used apply only to a narrow class of networks. On the other hand, any universal solution protocol must use Ω(n log n) moves in the worst case, regardless of the size of the team. A universal solution protocol has been recently presented that uses a team of just two agents with a map of the network, and locates a black hole in at most O(n log n) moves. Thus, this protocol has both optimal size and worstcaseoptimal cost. We show that this result, far from closing the research quest, can be significantly improved. In this paper we present a universal protocol that allows a team of two agents with a network map to locate the black hole using at most O(n+d log d) moves,whered is the diameter of the network. This means that, without losing its universality and without violating the worstcase Ω(n log n) lower bound, this algorithm allows two agents to locate a black hole with Θ(n) cost in a very large class of (possibly unstructured) networks.