Black Hole Search in Directed Graphs

Czyzowicz, Jurek; Dobrev, Štefan; Královič, Rastislav; Miklík, Stanislav; Pardubská, Dana

doi:10.1007/978-3-642-11476-2_15

Cited by 26 publications

(21 citation statements)

References 25 publications

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“…This black hole search problem has been originally studied in ring networks [12] and has been extensively investigated in various settings since then (e.g., see [4,6,8,10,13,14,19,24]). In order to locate the black hole, some of the agents of the team will necessarily have to enter the dangerous site.…”

Section: Related Workmentioning

confidence: 99%

“…The case of black links in arbitrary networks has been studied in [2,15], respectively for anonymous and non-anonymous nodes. Black hole search in directed graphs has been investigated for the first time in [4], where it is shown that the requirements in number of agents change considerably. A variant of dangerous node behavior has been studied in [22], where the authors introduce black holes with Byzantine behavior (they do not always destroy a passing agent) and consider the periodic ring exploration problem.…”

Section: Related Workmentioning

confidence: 99%

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Time Optimal Algorithms for Black Hole Search in Rings

Balamohan

Flocchini

Miri

et al. 2010

Combinatorial Optimization and Applications

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Abstract. In a network environments supporting mobile entities (called robots or agents), a black hole is harmful site that destroys any incoming entity without leaving any visible trace. The black-hole search problem is the task of a team of k > 1 mobile entities, starting from the same safe location and executing the same algorithm, to determine within finite time the location of the black hole. In this paper we consider the black hole search problem in asynchronous ring networks of n nodes, and focus on the time complexity. It is known that any algorithm for black-hole search in a ring requires at least 2(n − 2) time in the worst case. The best algorithm achieves this bound with a team of n − 1 agents with an average time cost 2(n − 2), equal to the worst case. In this paper we first show how the same number of agents using 2 extra time units from optimal in the worst case, can solve the problem in only 7 4 n − O(1) time on the average. We then prove that the optimal average case complexity 3 2 n − O(1) can be achieved without increasing the worst case using 2(n − 1) agents Finally we design an algorithm that achieves asymptotically optimal both worst case and average case time complexity employing an optimal team of k = 2 agents, thus improving on the earlier results that required O(n) agents.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Time Optimal Algorithms for Black Hole Search in Rings

Balamohan

Flocchini

Miri

et al. 2010

Combinatorial Optimization and Applications

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show abstract

“…Exploration of unlabeled and unknown digraphs using pebbles to mark vertices, has been studied by Bender et al [6]. A related problem of searching for a black hole has been recently studied for directed graphs (see [9]). …”

Section: Related Workmentioning

confidence: 99%

“…Exploration of unknown and unlabeled graphs (or digraphs) is difficult unless the agents are allowed to mark the nodes. As in several previous papers on the topic [3,4,9,11,13], we allow the agents to mark nodes of the digraphs by writing on whiteboards available at each node.…”

Section: Introductionmentioning

confidence: 99%

Rendezvous of Mobile Agents in Directed Graphs

Chalopin

Das

Widmayer

2010

Lecture Notes in Computer Science

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Abstract. We study the problem of gathering at the same location two mobile agents that are dispersed in an unknown and unlabeled environment. This problem called Rendezvous, is a fundamental task in distributed coordination among autonomous entities. Most previous studies on the subject model the environment as an undirected graph and the solution techniques rely heavily on the fact that an agent can backtrack on any edge it traverses. However, such an assumption may not hold for certain scenarios, for instance a road network containing one-way streets. Thus, we consider the case of strongly connected directed graphs and present the first deterministic solution for rendezvous of two anonymous (identical) agents moving in such a digraph. Our algorithm achieves rendezvous with detection for any solvable instance of the problem, without any prior knowledge about the digraph, not even its size.

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“…The problem has also been studied for co-located agents in directed graphs with whiteboards, both in the asynchronous [4] and synchronous cases [16]. A different dangerous behavior is studied for co-located agents in [17], where the authors consider a ring and assume black holes with Byzantine behavior, which do not always destroy a visiting agent.…”

Section: Introductionmentioning

confidence: 99%

Tight Bounds for Scattered Black Hole Search in a Ring

Chalopin

Das

Labourel

et al. 2011

Structural Information and Communication Complexity

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Abstract. We study the problem of locating a particularly dangerous node, the so-called black hole in a synchronous anonymous ring network with mobile agents. A black hole destroys all mobile agents visiting that node without leaving any trace. Unlike most previous research on the black hole search problem which employed a colocated team of agents, we consider the more challenging scenario when the agents are identical and initially scattered within the network. Moreover, we solve the problem with agents that have constant-sized memory and carry a constant number of identical tokens, which can be placed at nodes of the network. In contrast, the only known solutions for the case of scattered agents searching for a black hole, use stronger models where the agents have non-constant memory, can write messages in whiteboards located at nodes or are allowed to mark both the edges and nodes of the network with tokens. We are interested in the minimum resources (number of agents and tokens) necessary for locating all links incident to the black hole. In fact, we provide matching lower and upper bounds for the number of agents and the number of tokens required for deterministic solutions to the black hole search problem, in oriented or unoriented rings, using movable or unmovable tokens.

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Black Hole Search in Directed Graphs

Cited by 26 publications

References 25 publications

Time Optimal Algorithms for Black Hole Search in Rings

Time Optimal Algorithms for Black Hole Search in Rings

Rendezvous of Mobile Agents in Directed Graphs

Tight Bounds for Scattered Black Hole Search in a Ring

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