Automata, Languages and Programming
Volume 1099 of the series Lecture Notes in Computer Science pp 280289
Searching a fixed graph
 Elias KoutsoupiasAffiliated withCS Department, UCLA
 , Christos PapadimitriouAffiliated withEECS Department, UC Berkeley
 , Mihalis YannakakisAffiliated withBell Laboratories
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 worstcase 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 graphtheoretic parameters are NPcomplete —and MAXSNPhard — 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.
 Title
 Searching a fixed graph
 Book Title
 Automata, Languages and Programming
 Book Subtitle
 23rd International Colloquium, ICALP '96 Paderborn, Germany, July 8–12, 1996 Proceedings
 Pages
 pp 280289
 Copyright
 1996
 DOI
 10.1007/3540614400_135
 Print ISBN
 9783540614401
 Online ISBN
 9783540685807
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1099
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
 Additional Links
 Topics
 Industry Sectors
 Editors
 Authors

 Elias Koutsoupias ^{(1)}
 Christos Papadimitriou ^{(2)}
 Mihalis Yannakakis ^{(3)}
 Author Affiliations

 1. CS Department, UCLA, USA
 2. EECS Department, UC Berkeley, USA
 3. Bell Laboratories, 07974, Murray Hill, NJ
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