Maximum Edge-Disjoint Paths in k-Sums of Graphs

Chandra Chekuri, Guyslain Naves, F. Bruce Shepherd

Abstract: We consider the approximability of the maximum edge-disjoint paths problem (MEDP) in undirected graphs, and in particular, the integrality gap of the natural multicommodity flow based relaxation for it. The integrality gap is known to be \(\Omega(\sqrt{n})\) even for planar graphs [11] due to a simple topological obstruction and a major focus, following earlier work [14], has been understanding the gap if some constant congestion is allowed. In planar graphs the integrality gap is O(1) with congestion 2 [19,5]. In general graphs, recent work has shown the gap to be O(polylog(n)) [8,9] with congestion 2. Moreover, the gap is Ω(logΩ(c) n) in general graphs with congestion c for any constant c ≥ 1 [1].