, Volume 37, Issue 3, pp 165–186 | Cite as

A Distributed Ant Algorithm for\protect Efficiently Patrolling a Network

  • Vladimir  YanovskiEmail author
  • Israel A.  WagnerEmail author
  • Alfred M.  BrucksteinEmail author


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.

Ant algorithms Euler cycle Blanket time Graph algorithms 


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  1. 1.
    Y. Afek, E. Gafni, DistributedGoogle Scholar
  2. 2.
    R. Aleliunas, R. M. Karp, R. J. Lipton, L. Lovász, C. Rackoff, Random Walks, Universal Traversal Sequences and the Complexity of Maze Problems, Proceedings of the 20th Annual Symposium on Foundation of Computer Science, pp. 218–223, 1979. Google Scholar
  3. 3.
    K. Knight, Are Many Reactive Agents Better than a Few Deliberative Ones, Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI), pp. 432–437, 1993. Google Scholar
  4. 4.
    D. Hearn, M. Pauline Baker, Computer Graphics, Second Edition, Prentice Hall, 1994 Google Scholar
  5. 5.
    S. Koenig, Complexity of Edge Counting, in: Goal-Directed Acting with Incomplete Information, Technical Report CMU-CS-97-199, School of Computer Science, Carnegie Mellon University, November 1997. Google Scholar
  6. 6.
    S. Koenig, R. G. Simmons, Easy and Hard Testbeds for Real-Time Search Algorithms, Proceedings of the National Conference on Artificial Intelligence, pp. 279–285, 1996. Google Scholar
  7. 7.
    Koenig, S., Szymanski, B., Liu, Y. 2001Efficient and Inefficient Ant Coverage MethodsAnnals of Mathematics and Artificial Intelligence314176CrossRefGoogle Scholar
  8. 8.
    Korf, R. E. 1992Real-Time Heuristic SearchArtificial Intelligence42189211CrossRefGoogle Scholar
  9. 9.
    Rivest, R. L., Shamir, A. 1982How to Reuse a “Write-Once” MemoryInformation and Control55119zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Tarjan, R. 1972Depth-First Search and Linear Graph AlgorithmsSIAM Journal on Computing1146160zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    I. A. Wagner and A. M. Bruckstein, Cooperative Cleaners - a Study in Ant Robotics, in: A. Paulraj, V. Roychowdhry, C. D. Schaper - ed., Communication, Computation, Control and Signal Processing: A Tribute to Thomas Kailath, Kluwer Academic Publishers, The Netherlands, 1997 Google Scholar
  12. 12.
    Wagner, I. A., Lindenbaum, M., Bruckstein, A. M. 1998Efficiently Searching a Graph by a Smell-Oriented Vertex ProcessAnnals of Mathematics and Artificial Intelligence24211223zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    I. A. Wagner, M. Lindenbaum, A. M. Bruckstein, Smell as a Computational Resource—a Lesson We Can Learn from the Ants, Proceedings of ISTCS ‘96, Jerusalem, pp. 219–230, 1996. Google Scholar
  14. 14.
    Wagner, I. A., Lindenbaum, M., Bruckstein, A. M. 1999Distributed Covering by Ant-Robots Using Evaporating TracesIEEE Transactions on Robotics and Automation15918933CrossRefGoogle Scholar
  15. 15.
    I. A. Wagner, M. Lindenbaum, A. M. Bruckstein, On-Line Graph Searching by a Smell-Oriented Vertex Process, AAAI-97, Workshop on On-Line Search, Providence, RI, 1997. Google Scholar

Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  1. 1.Computer Science Department, Technion IIT, Haifa 32000Israel
  2. 2.IBM Haifa Research Laboratory, MATAM, Haifa 31905Israel

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