On the Complexity of the Crossing Contact Map Pattern Matching Problem

Abstract

Contact maps are concepts that are often used to represent structural information in molecular biology. The contact map pattern matching (CMPM) problem is to decide if a contact map (called the pattern) is a substructure of another contact map (called the target). In general, the problem is NP-hard, but when there are restrictions on the form of the pattern, the problem can, in some case, be solved in polynomial time. In particular, a polynomial time algorithm has been proposed [1] for the case when the patterns are so-called crossing contact maps. In this paper we show that the problem is actually NP-hard, and show a flaw in the proposed polynomial-time algorithm. Through the same method, we also show that a related problem, namely, the 2-interval patten matching problem with $\{<, \between\}$ -structured patterns and disjoint interval ground set, is NP-hard.