Computing Maximum Mean Cuts

Most primal minimum cost network flow (MCNF) algorithms can be seen as variants on cancelling negative augmenting cycles. The analogous view of dual MCNF algorithms is that they cancel positive augmenting cuts. In a companion paper we show that if a dual algorithm chooses to cancel cuts which have the greatest rate of increase in dual objective value per arc, which are called maximum mean cuts, a strongly polynomial algorithm results. However, this result depends on being able to compute maximum mean cuts in polynomial time. In this paper we present an efficient parametric algorithm that computes maximum mean cuts by doing O ( min { n, log(nU) 1+log log(nU)−log log n }) min cut calculations (these bounds are due to Radzik [30]), where U is the largest absolute arc capacity.