Greedy-edge-disjoint paths in complete graphs

Abstract

The maximum edge-disjoint paths problem (MEDP) is one of the most classical NP-hard problems. We study the approximation ratio of a simple and practical approximation algorithm, the shortest-path-first greedy algorithm (SGA), for MEDP in complete graphs.Previously, it was known that this ratio is at most 54. Adapting results by Kolman and Scheideler [Proceedings of SODA, 2002, pp. 184--193], we show that SGA achieves approximation ratio 8F+1 for MEDP in undirected graphs with flow number F and, therefore, has approximation ratio at most 9 in complete graphs. Furthermore, we construct a family of instances that shows that SGA cannot be better than a 3-approximation algorithm. Our upper and lower bounds hold also for the bounded-length greedy algorithm, a simple on-line algorithm for MEDP.