Algorithms for shortest paths and d-cycle problems

Authors:
Sergei Bespamyatnikh;Andrei Kelarev
Affiliations:
Department of Computer Science, University of British Columbia, Vancouver, BC Canada V6T 1Z4;Faculty of Science and Engineering, University of Tasmania, GPO Box 252-37, Hobart, Tasmania 7001, Australia
Venue:
Journal of Discrete Algorithms
Year:
2003

Citing 5
Cited 0

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Abstract

Let G be a weighted graph with n vertices and m edges. We address the d-cycle problem, i.e., the problem of finding a subgraph of minimum weight with given cyclomatic number d. Hartvigsen [Minimum path bases, J. Algorithms 15 (1993) 125-142] presented an algorithm with running time O(n2m) and O(n2d-1m2) for the cyclomatic numbers d = 1 and d ≥ 2, respectively. Using a (d + 1)-shortest-paths algorithm, we develop a new more efficient algorithm for the d-cycle problem with running time O(n2d-1 + n2m + n3 log n).