Fingerprint clustering with bounded number of missing values

Abstract

The problem of clustering fingerprint vectors with missing values is an interesting problem in Computational Biology that has been proposed in [6], In this paper we show some improvements in closing the gaps between the known lower bounds and upper bounds on the approximability of variants of the biological problem. Moreover, we have studied two additional variants of the original problem. We prove that all such problems are APX-hard even when each fingerprint contains only two unknown positions and we present a greedy algorithm that has constant approximation factors for these variants. Despite the hardness of these restricted versions of the problem, we show that the general clustering problem on an unbounded number of missing values such that they occur for every fixed position of an input vector in at most one fingerprint is polynomial time solvable. © Springer-Verlag Berlin Heidelberg 2006.