Algorithms for shortest paths and d-cycle problems

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(n2 m) and O(n2-1 m) 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 +n2 m + n3 logn). © 2003 Elsevier B.V. All rights reserved.