Hardness of routing for minimizing superlinear polynomial cost in directed graphs

Abstract

We study the problem of routing in directed graphs with superlinear polynomial costs, which is significant for improving the energy efficiency of networks. In this problem, we are given a directed graph G(V, E) and a set of traffic demands. Routing (formula presented) units of demands along an edge e will incur a cost of (formula presented). The objective is to find integral routing paths for minimizing (formula presented). Through developing a new labeling technique and applying it to a randomized reduction, we prove an (formula presented) hardness factor for this problem under the assumption that (formula presented).