On the complexity of finding emerging patterns
Emerging patterns have been studied as a useful type of pattern for the diagnosis and understanding of diseases based on the analysis of gene expression profiles. They are useful for capturing interactions among genes (or other biological entities), for capturing signature patterns for disease subtypes, and deriving potential disease treatment plans, etc. In this paper we study the complexity of finding emerging patterns (with the highest frequency). We first show that the problem is MAX SNP-hard. This implies that polynomial time approximation schemes do not exist for the problem unless P = NP. We then prove that for any constant delta < 1, the emerging pattern problem cannot be approximated within ratio 2(log delta) n in polynomial time unless NP subset of DTIME[2(polylog n)], where n is the number of positions in a pattern. (c) 2005 Elsevier B.V. All rights reserved.
emerging pattern inapproximability