A Recursive Approach to Multi-robot Exploration of Trees

  • Christian Ortolf
  • Christian Schindelhauer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8576)

Abstract

The multi-robot exploration problem is to explore an unknown graph of size n and depth d with k robots starting from the same node. For known graphs a traversal of all nodes takes at most \({\cal O}(d + n/k)\) steps. The ratio between the time until cooperating robots explore an unknown graph and the optimal traversal of a known graph is called the competitive exploration time ratio.

It is known that for any algorithm this ratio is at least \(\Omega\left((\log k)/\log \log k\right)\). For k ≤ n robots the best algorithm known so far achieves a competitive time ratio of \({\cal O}\left({k}/{\log k} \right)\).

Here, we improve this bound for trees with bounded depth or a minimum number of robots. Starting from a simple \({\cal O}(d)\)-competitive algorithm, called Yo-yo, we recursively improve it by the Yo-star algorithm, which for any 0 < α < 1 transforms a g(d,k)-competitive algorithm into a \({\cal O}( (g(d^{\alpha},k) \log k + d^{1-\alpha})(\log k + \log n))\)-competitive algorithm. So, we achieve a competitive bound of \({\cal O}\left(2^{{\cal O}(\sqrt{(\log d)(\log\log k)})}(\log k)(\log k+ \log n)\right)\). This improves the best known bounds for trees of depth d, whenever the number of robots is at least \( k=2^{\omega(\sqrt{(\log d)(\log \log d)})}\) and \(n=2^{O(2^{\sqrt{\log d}})}\).

Keywords

competitive analysis robot collective graph exploration 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Christian Ortolf
    • 1
  • Christian Schindelhauer
    • 1
  1. 1.Department of Computer Science, Computer NetworksUniversity of FreiburgGermany

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