On finding a shortest path in circulant graphs with two jumps

Authors:
Domingo Gómez;Jaime Gutierrez;Álvar Ibeas;Carmen Martínez;Ramón Beivide
Affiliations:
Faculty of Sciences, University of Cantabria, Santander, Spain;Faculty of Sciences, University of Cantabria, Santander, Spain;Faculty of Sciences, University of Cantabria, Santander, Spain;Faculty of Sciences, University of Cantabria, Santander, Spain;Faculty of Sciences, University of Cantabria, Santander, Spain
Venue:
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Year:
2005

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Abstract

In this paper we present algorithms for finding a shortest path between two vertices of any weighted undirected and directed circulant graph with two jumps. Our shortest path algorithm only requires O(log N) arithmetic steps and the total bit complexity is O(log3N), where N is the number of the graph’s vertices. This method has been derived from some Closest Vector Problems (CVP) of lattices in dimension two and with ℓ1-norm.