Congestion minimization is a well-known routing problem for which

there is an O(log n/loglog n)-approximation via randomized rounding due to Raghavan and Thompson. Srinivasan formally introduced the low-congestion multi-path routing problem as a generalization of the (single-path) congestion minimization problem. The goal is to route multiple disjoint paths for each pair, for the sake of fault tolerance. Srinivasan developed a dependent randomized scheme for a special case of the multi-path problem when the input consists of a given set of disjoint paths for each pair and the goal is to select a given subset of them. Subsequently Doerr gave a different dependentrounding scheme and derandomization. Doerr et al. considered the problem where the paths have to be chosen, and applied the dependent rounding technique and evaluated it experimentally. However, their algorithm does not maintain the required disjointness property without which the problem easily reduces to the standard congestion minimization problem.

In this note we show a simple algorithm that solves the problem

correctly without the need for dependent rounding --- standard

independent rounding suffices. This is made possible via the notion

of multiroute flows originally suggested by Kishimoto et al. One advantage of the simpler rounding is an improved bound on the congestion when the path lengths are short.