Minimum cycle bases for network graphs

The minimum cycle basis problem in a graph G = (V,E) is the task to construct a minimum length basis of its cycle vector space. A well-known algorithm by Horton of 1987 needs running time O(|V||E|^2.376). We present a new combinatorial approach which generates minimum cycle bases in time O(max{|E|³,|E||V|²log |V|}) with a space requirement of Θ(|E|²). This method is especially suitable for large sparse graphs of electric engineering applications since there, typically, |E| is close to linear in |V|.