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A Distributed Ant Algorithm for\protect Efficiently Patrolling a Network

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Abstract

We consider the problem of patrolling—i.e. ongoing exploration of a network by a decentralized group of simple memoryless robotic agents. The model for the network is an undirected graph, and our goal, beyond complete exploration, is to achieve close to uniform frequency of traversal of the graph’s edges. A simple multi-agent exploration algorithm is presented and analyzed. It is shown that a single agent following this procedure enters, after a transient period, a periodic motion which is an extended Eulerian cycle, during which all edges are traversed an identical number of times. We further prove that if the network is Eulerian, a single agent goes into an Eulerian cycle within 2|E|D steps, |E| being the number of edges in the graph and D being its diameter. For a team of k agents, we show that after at most 2( 1 + 1/k) |E|D steps the numbers of edge visits in the network are balanced up to a factor of two. In addition, various aspects of the algorithm are demonstrated by simulations.

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Authors and Affiliations

  1. Computer Science Department, Technion IIT, Haifa 32000, Israel

    Vladimir Yanovski, Israel A. Wagner & Alfred M. Bruckstein

  2. IBM Haifa Research Laboratory, MATAM, Haifa 31905, Israel

    Israel A. Wagner

Authors
  1. Vladimir Yanovski
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  2. Israel A. Wagner
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  3. Alfred M. Bruckstein
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Corresponding authors

Correspondence to Vladimir Yanovski, Israel A. Wagner or Alfred M. Bruckstein.

Additional information

Communicated by N. Megiddo.

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Yanovski, V., Wagner, I. & Bruckstein, A. A Distributed Ant Algorithm for\protect Efficiently Patrolling a Network. Algorithmica 37, 165–186 (2003). https://doi.org/10.1007/s00453-003-1030-9

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  • DOI: https://doi.org/10.1007/s00453-003-1030-9

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