Elias Koutsoupias
Professor of Computer Science
University of Athens
Panepistimiopolis, Ilissia
Athens 15784

phone: +30 210 7275122
fax: +30 210 7275114

E. Koutsoupias, C. Papadimitriou, and M. Yannakakis. Searching a fixed graph. In International Colloquium on Automata, Languages, and Programming, pages 280--289, Paderborn, Germany, 8--12 July 1996.
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We study three combinatorial optimization problems related to searching a graph that is known in advance, for an item that resides at an unknown node. The search ratio of a graph is the optimum competitive ratio (the worst-case ratio of the distance traveled before the unknown node is visited, over the distance between the node and a fixed root, minimized over all Hamiltonian walks of the graph). We also define the randomized search ratio (we minimize over all distributions of permutations). Finally, the traveling repairman problem seeks to minimize the expected time of visit to the unknown node, given some distribution on the nodes. All three of these novel graph-theoretic parameters are NP-complete ---and MAXSNP-hard--- to compute exactly; we present interesting approximation algorithms for each. We also show that the randomized search ratio and the traveling repairman problem are related via duality and polyhedral separation.


@string{ICALP96 = {International Colloquium on Automata, Languages,
                  and Programming}}

  author =       {E. Koutsoupias and C. Papadimitriou and M. Yannakakis},
  title =        {Searching a fixed graph},
  booktitle =    ICALP96,
  pages =        {280--289},
  address =      {Paderborn, Germany},
  month =        {8--12 } # jul,
  year =         1996