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Black Hole Search in Directed Graphs

  • Conference paper
Structural Information and Communication Complexity (SIROCCO 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5869))

Abstract

We consider the problem of cooperative network exploration by agents under the assumption that there is a harmful host present in the network that destroys the incoming agents without outside trace – the so-called black hole search problem.

Many variants of this problem have been studied, with various assumptions about the timing, agents’ knowledge about the topology, means of inter-agent communication, amount of writable memory in vertices, and other parameters. However, all this research considered undirected graphs only, and relied to some extent on the ability of an agent to mark an edge as safe immediately after having traversed it.

In this paper we study directed graphs where this technique does not apply, and show that the consequence is an exponential gap: While in undirected graphs Δ + 1 agents are always sufficient, in the directed case at least 2Δ agents are needed in the worst case, where Δ is in-degree of the black hole. This lower bound holds also in the case of synchronous agents. Furthermore, we ask the question What structural information is sufficient to close this gap? and show that in planar graphs with a planar embedding known to the agents, 2Δ + 1 agents are sufficient, and 2Δ agents are necessary.

Research supported by grant APVV-0433-06.

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Author information

Authors and Affiliations

  1. Université du Québec en Outaouais, Gatineau, Québec, Canada

    Jurek Czyzowicz

  2. Slovak Academy of Sciences, Bratislava, Slovakia

    Stefan Dobrev

  3. Comenius University, Bratislava, Slovakia

    Rastislav Královič, Stanislav Miklík & Dana Pardubská

Authors
  1. Jurek Czyzowicz
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  2. Stefan Dobrev
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  3. Rastislav Královič
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  4. Stanislav Miklík
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  5. Dana Pardubská
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Editor information

Editors and Affiliations

  1. Technion – Israel Institute of Technology, Dept. of Industrial Engineering and Management,, Technion City, 32000, Haifa, Israel

    Shay Kutten

  2. Faculty of Mechanical Engineering, University of Maribor, FS, Smetanova 17, 2000, Maribor, Slovenia

    Janez Žerovnik

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Czyzowicz, J., Dobrev, S., Královič, R., Miklík, S., Pardubská, D. (2010). Black Hole Search in Directed Graphs. In: Kutten, S., Žerovnik, J. (eds) Structural Information and Communication Complexity. SIROCCO 2009. Lecture Notes in Computer Science, vol 5869. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11476-2_15

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  • DOI: https://doi.org/10.1007/978-3-642-11476-2_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11475-5

  • Online ISBN: 978-3-642-11476-2

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