Algorithms for Generating Fundamental Cycles in a Graph

The following problem is considered: Given an undirected, connected graph G, find a spanning tree in G such that the sum of the lengths of the fundamental cycles (with respect to this tree) is minimum. This problem, besides being interesting in its own right, is useful in a variety of situations It is shown that this problem is NP-complete. A number of polynomial-time, heuristic algorithms which yield "good" suboptimal solutions are presented and their performances are discussed. Finally, it is shown that for regular graphs of order n the expected value of the total length of a minimum fundamentalcycle set does not exceed O(n2).

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