On random quadratic bottleneck assignment problems

Abstract

The relative error between best and worst solution of quadratic bottleneck assignment problems with cost coefficientsd _ijpq =a _ip b _jq is considered, wherea _ip is either arbitrarily given or corresponds to a distance in the plane. It is shown that the relative error is bounded by a function∈(m), tending to zero, with probability tending to one asm → ∞, provided the data are uniformly distributed. This implies that any algorithm for the above mentioned problems yields asymptotically an arbitrarily small relative error with probability tending to one.