On routing in circulant graphs

Authors:
Jin-Yi Cai;George Havas;Bernard Mans;Ajay Nerurkar;Jean-Pierre Seifert;Igor Shparlinski
Affiliations:
Department of Computer Science and Engineering, State University of NY at Buffalo, Buffalo, NY;Centre for Discrete Mathematics and Computing, Department of Computer Science and Electrical Engineering, he University of Queensland, Qld, Australia;Department of Computing, Macquarie University, Sydney, NSW, Australia;Department of Computer Science and Engineering, State University of NY at Buffalo, Buffalo, NY;Department of Mathematics and Computer Science, University of Frankfurt, Frankfurt on the Main, Germany;Department of Computing, Macquarie University, Sydney, NSW, Australia
Venue:
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Year:
1999

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Abstract

We investigate various problems related to circulant graphs -finding the shortest path between two vertices, finding the shortest loop, and computing the diameter. These problems are related to shortest vector problems in a special class of lattices. We give matching upper and lower bounds on the length of the shortest loop. We claim NP-hardness results, and establish a worst-case/average-case connection for the shortest loop problem. A pseudo-polynomial time algorithm for these problems is also given. Our main tools are results and methods from the geometry of numbers.