Solving the Order-Preserving Submatrix Problem via Integer Programming

Authors:
Andrew C. Trapp;Oleg A. Prokopyev
Affiliations:
Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261;Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261
Venue:
INFORMS Journal on Computing
Year:
2010

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Abstract

In this paper we consider the order-preserving submatrix (OPSM) problem. This problem is known to be NP-hard. Although in recent years some heuristic methods have been presented to find OPSMs, they lack the guarantee of optimality. We present exact solution approaches based on linear mixed 0--1 programming formulations and develop algorithmic enhancements to aid in solvability. Encouraging computational results are reported both for synthetic and real biological data. In addition, we discuss theoretical computational complexity issues related to finding fixed patterns in matrices.