Searching a fixed graph

  • Elias Koutsoupias
  • Christos Papadimitriou
  • Mihalis Yannakakis
Session 6: Graph Algorithms

DOI: 10.1007/3-540-61440-0_135

Part of the Lecture Notes in Computer Science book series (LNCS, volume 1099)
Cite this paper as:
Koutsoupias E., Papadimitriou C., Yannakakis M. (1996) Searching a fixed graph. In: Meyer F., Monien B. (eds) Automata, Languages and Programming. ICALP 1996. Lecture Notes in Computer Science, vol 1099. Springer, Berlin, Heidelberg

Abstract

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.

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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Elias Koutsoupias
    • 1
  • Christos Papadimitriou
    • 2
  • Mihalis Yannakakis
    • 3
  1. 1.CS DepartmentUCLAUSA
  2. 2.EECS DepartmentUC BerkeleyUSA
  3. 3.Bell LaboratoriesMurray Hill

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