Poly-logarithmic Approximation for Maximum Node Disjoint Paths with Constant Congestion

We consider the Maximum Node Disjoint Paths (MNDP) problem in undirected graphs. The input consists of an undirected graph G = (V,E) and a collection {(s1, t1), . . . , (sk, tk)} of k source-sink pairs. The goal is to select a maximum cardinality subset of pairs that can be routed/connected via node-disjoint paths. A relaxed version of MNDP allows up to c paths to use a node, where c is the congestion parameter. We give a polynomial time algorithm that routes Ω(OPT/poly log k) pairs with O(1) congestion, where OPT is the value of an optimum fractional solution to a natural multicommodity flow relaxation. Our result builds on the recent breakthrough of Chuzhoy [17] who gave the first poly-logarithmic approximation with constant congestion for the Maximum Edge Disjoint Paths (MEDP) problem.