Hardness of Directed Routing with Congestion

Given a graph G and a collection of source-sink pairs in G, what is the least integer c such that each source can be connected by a path to its sink, with at most c paths going through an edge? This is known as the congestion minimization problem, and the quantity c is called the congestion. Congestion minimization is one of the most well-studied NP-hard optimization problems. It is well-known that the elegant randomized rounding technique of Raghavan and Thompson can be used to obtain a solution with congestion at most c + O( log n log log n ) where c is the optimal congestion. In this paper we show that there exists a > 0 such that no polynomial-time algorithm can guarantee a solution with congestion c + ( log n log log n ) unless NP is contained in ZPTIME(nlog log n ). We also study the directed edge-disjoint paths (EDP) problem with congestion. The input to this problem is a graph G and a collection of source-sink pairs in G, along with a congestion parameter c. The goal now ...

• Type: Journal
• Year: 2006
• Where: ECCC
• Authors: Julia Chuzhoy, Sanjeev Khanna
• Keywords: Congestion Minimization, Congestion Minimization Problem, ECCC 2006, Source-sink Pair