Approximation Algorithms for the Edge-Disjoint Paths Problem via Raecke Decompositions

Abstract

We study the Edge-Disjoint Paths with Congestion (EDPwC) problem in undirected networks in which we must integrally route a set of demands without causing large congestion on an edge. We present a $(polylog(n), poly(\log\log n))$-approximation, which means that if there exists a solution that routes $X$ demands integrally on edge-disjoint paths (i.e. with congestion $1$), then the approximation algorithm can route $X/polylog(n)$ demands with congestion $poly(\log\log n)$. The best previous result for this problem was a $(n^{1/\beta}, \beta)$-approximation for $\beta