An explicit upper bound for the approximation ratio of the maximum gene regulatory network problem

Abstract

One of the combinatorial models for the biological problem of inferring gene regulation networks is the MAXIMUM GENE REGULATORY NETWORK PROBLEM, shortly MGRN, proposed in [2]. The problem is NP-hard [2], consequently the attention has shifted towards approximation algorithms, leading to a polynomial-time 1/2-approximation algorithm [2], while no upper bound on the possible approximation ratio was previously known. In this paper we make a first step towards closing the gap between the best known and the best possible approximation factors, by showing that no polynomial-time approximation algorithm can have a factor better than 1 - 1/8/1+e2 unless RP=NP. © Springer-Verlag Berlin Heidelberg 2005.