Implementing Minimum Cycle Basis Algorithms

Abstract. In this paper we consider the problem of computing a minimum cycle basis of an undirected graph G = (V, E) with n vertices and m edges. We describe an efficient implementation of an O(m3 + mn2 log n) algorithm presented in [1]. For sparse graphs this is the currently best known algorithm. This algorithm’s running time can be partitioned into two parts with time O(m3 ) and O(m2 n + mn2 log n) respectively. Our experimental findings imply that the true bottleneck of a sophisticated implementation is the O(m2 n + mn2 log n) part. A straightforward implementation would require Ω(nm) shortest path computations, thus we develop several heuristics in order to get a practical algorithm. Our experiments show that in random graphs our techniques result in a significant speedup. Based on our experimental observations, we combine the two fundamentally different approaches to compute a minimum cycle basis used in [1, 2] and [3, 4], to obtain a new hybrid algorithm with running time...

• Type: Conference
• Year: 2005
• Where: WEA
• Authors: Kurt Mehlhorn, Dimitrios Michail
• Keywords: Algorithms, Minimum Cycle Basis, Undirected Graph, WEA 2005