Minimum Cycle Bases of Weighted Outerplanar Graphs

Authors:
Tsung-Hao Liu;Hsueh-I. Lu
Affiliations:
Department of Computer Science and Information Engineering, National Taiwan University,;Department of Computer Science and Information Engineering, National Taiwan University,
Venue:
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Year:
2009

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Abstract

We give the first known optimal algorithm that computes a minimum cycle basis for any weighted outerplanar graph. Specifically, for any n-node edge-weighted outerplanar graph G, we give an O(n)-time algorithm to obtain an O(n)-space compact representation Z(驴) for a minimum cycle basis 驴 of G. Each cycle in 驴 can be computed from Z(驴) in O(1) time per edge. Our result works for directed and undirected outerplanar graphs G.