Optimal routing in double loop networks

Authors:
Domingo Gómez;Jaime Gutierrez;Álvar Ibeas
Affiliations:
Faculty of Sciences, University of Cantabria, E39071 Santander, Spain;Faculty of Sciences, University of Cantabria, E39071 Santander, Spain;Faculty of Sciences, University of Cantabria, E39071 Santander, Spain
Venue:
Theoretical Computer Science
Year:
2007

Citing 24
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Abstract

In this paper, we study the problem of finding the shortest path in circulant graphs with an arbitrary number of jumps. We provide algorithms specifically tailored for weighted undirected and directed circulant graphs with two jumps which compute the shortest path. Our method only requires O(logN) arithmetic operations and the total bit complexity is O(log^2NloglogNlogloglogN), where N is the number of the graph's vertices. This elementary and efficient shortest path algorithm has been derived from the Closest Vector Problem (CVP) of lattices in dimension two and with an @?"1 norm.