On Set Covering Based on Biclustering

Abstract

In this paper, we present a clustering heuristic for solving demand covering models where the objective is to determine locations for servers that optimally cover a given set of demand points. This heuristic is based on the concept of biclusters and processes the set of demand points as well as the set of potential servers and determines biclusters that result in smaller problems. Given a coverage matrix, a bicluster is defined as a sub-matrix spanned by both a subset of rows and a subset of columns, such that rows are the most similar to each other when compared over columns. The algorithm starts by using any biclustering algorithm in order to identify appropriate biclusters of the coverage matrix and then combines selected biclusters to define an aggregate solution to the original problem. The algorithm can be easily adapted to address a whole family of covering problems including set covering, maximal covering and backup covering problems. The proposed algorithm is tested in a series of widely known test datasets for various such problems. The main objective of this paper is to introduce the concept of biclustering as an efficient and effective approach to tackle covering problems and to stimulate further research in this area.