Searching for a Black Hole in Tree Networks

Czyzowicz, Jurek; Kowalski, Dariusz R.; Μάρκου, Ευριπίδης; Pełc, Andrzej

doi:10.1007/11516798_5

Cited by 25 publications

(28 citation statements)

References 6 publications

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“…We consider here malicious hosts of a particularly harmful nature, called black holes [3,2,4,5,6]. A black hole is a node in a network which contains a stationary process destroying all mobile agents visiting this node, without leaving any trace on the other nodes of the network.…”

Section: Introductionmentioning

confidence: 99%

Approximation bounds for Black Hole Search problems

et al. 2008

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Abstract:A black hole is a highly harmful stationary process residing in a node of a network and destroying all mobile agents visiting the node without leaving any trace. The Black Hole Search is the task of locating all black holes in a network, through the exploration of its nodes by a set of mobile agents. In this paper we consider the problem of designing the fastest Black Hole Search, given the map of the network, the starting node and a subset of nodes of the network initially known to be safe. We study the version of this problem that assumes that there is at most one black hole in the network and there are two agents, which move in synchronized steps. We prove that this problem is not polynomial-time approximable within any constant factor less than 389 388 (unless P=NP). We give a 6-approximation algorithm, thus improving on the 9.3-approximation algorithm from [3]. We also prove APX-hardness for a restricted version of the problem, in which only the starting node is initially known to be safe.

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Section: Introductionmentioning

confidence: 99%

Approximation bounds for Black Hole Search problems

et al. 2008

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“…An agent X may infer the location of a black hole, if it expects to meet another agent Y , but agent Y does not show up. This model, but with the added restriction that there are only two agents and at most one black hole, has been previously studied in [1,2,8,9]. Those papers give NP-hardness results and approximation algorithms for the problem of calculating an optimal (shortest) traversal schedules.…”

Section: Introductionmentioning

confidence: 99%

Searching for Black-Hole Faults in a Network Using Multiple Agents

Cooper

Klasing

Radzik

2006

Lecture Notes in Computer Science

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Abstract. We consider a fixed communication network where (software) agents can move freely from node to node along the edges. A black hole is a faulty or malicious node in the network such that if an agent enters this node, then it immediately "dies." We are interested in designing an efficient communication algorithm for the agents to identify all black holes. We assume that we have k agents starting from the same node s and knowing the topology of the whole network. The agents move through the network in synchronous steps and can communicate only when they meet in a node. At the end of the exploration of the network, at least one agent must survive and must know the exact locations of the black holes. If the network has n nodes and b black holes, then any exploration algorithm needs Ω(n/k + D b ) steps in the worstcase, where D b is the worst case diameter of the network with at most b nodes deleted. We give a general algorithm which completes exploration in O((n/k) log n/ log log n+bD b ) steps for arbitrary networks, if b ≤ k/2. In the case when, we give a refined algorithm which completes exploration in asymptotically optimal O(n/k) steps.

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“…Due to its nature, the site where such a process is located is called a black hole (e.g., [2,3,5,4,6,12]). …”

Section: The Problemmentioning

confidence: 99%

“…The BLACK HOLE SEARCH problem has been studied also in synchronous settings, where the time for an agent to traverse a link is assumed to be unitary; in this case, tight bounds have been established for some classes of trees [2]. In the case of general networks, approximation algorithms have been described in [2] and subsequently improved [12].…”

Section: Related Workmentioning

confidence: 99%