Tight Lower Bound for the Channel Assignment Problem

Abstract

We study the complexity of the C hannel A ssignment problem. An open problem asks whether C hannel A ssignment admits an O ( c n ) (times a polynomial in the bit size) time algorithm, where n is a number of the vertices, for a constant c independent of the weights on the edges. We answer this question in the negative. Indeed, we show that in the standard Word RAM model, there is no 2 o ( n log n ) (times a polynomial in the bit size) time algorithm solving C hannel A ssignment unless the exponential time hypothesis fails. Note that the currently best known algorithm works in time O *( n !) = 2 O ( n log n ) , so our lower bound is tight (where the O *() notation suppresses polynomial factors).