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Online graph exploration algorithms for cycles and trees by multiple searchers

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Abstract

This paper deals with online graph exploration problems by multiple searchers. The information on the graph is given online. As the exploration proceeds, searchers gain more information on the graph. Assuming an appropriate communication model among searchers, searchers can share the information about the environment. Thus, a searcher must decide which vertex to visit next based on the partial information on the graph gained so far by searchers. We assume that all searchers initially start the exploration at the origin vertex, and the goal is that each vertex is visited by at least one searcher and all searchers finally return to the origin vertex. The objective is to minimize the time when the goal is achieved. We study the case of cycles and trees. For the former, we give an optimal online exploration algorithm in terms of competitive ratio, and for the latter, we also give an online exploration algorithm which is optimal among greedy algorithms.

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Acknowledgments

The second author is supported by JSPS Grant-in-Aid for Scientific Research(B) (21300003). The fourth author is supported by Grant-in-Aid for JSPS Research Fellowships for Young Scientists.

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Authors and Affiliations

  1. Department of Architecture and Architectural Engineering, Kyoto University, Nishikyo-ku, Kyoto, 615-8540, Japan

    Yuya Higashikawa & Naoki Katoh

  2. Département d’Informatique, Université Libre de Bruxelles, Brussels, Belgium

    Stefan Langerman

  3. Research Institute for Mathematical Sciences, Kyoto University, Sakyo-ku, Kyoto, 606-8502, Japan

    Shin-ichi Tanigawa

Authors
  1. Yuya Higashikawa
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  2. Naoki Katoh
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  3. Stefan Langerman
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  4. Shin-ichi Tanigawa
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Correspondence to Yuya Higashikawa.

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Higashikawa, Y., Katoh, N., Langerman, S. et al. Online graph exploration algorithms for cycles and trees by multiple searchers . J Comb Optim 28, 480–495 (2014). https://doi.org/10.1007/s10878-012-9571-y

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  • DOI: https://doi.org/10.1007/s10878-012-9571-y

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