Optimal lower bound for generalized median problems in metric space

Abstract

The computation of generalized median patterns is typically an NP-complete task. Therefore, research efforts are focused on approximate approaches. One essential aspect in this context is the assessment of the quality of the computed approximate solutions. In this paper we present a lower bound in terms of a linear program for this purpose. It is applicable to any pattern space. The only assumption we make is that the distance function used for the definition of generalized median is a metric. We will prove the optimality of the lower bound, i.e. it will be shown that no better one exists when considering all possible instances of generalized median problems. An experimental verification in the domain of strings and graphs shows the tightness, and thus the usefulness, of the proposed lower bound.