A Fixed Parameter Tractable Integer Program for Finding the Maximum Order Preserving Submatrix

Jens Humrich, Thomas Gärtner, Gemma C. Garriga

Abstract: Order-preserving sub matrices are an important tool for the analysis of gene expression data. As finding large order-preserving sub matrices is a computationally hard problem, previous work has investigated both exact but exponential-time as well as polynomial-time but inexact algorithms for finding large order-preserving sub matrices. In this paper, we propose a novel exact algorithm to find maximum order preserving sub matrices which is fixed parameter tractable with respect to the number of columns of the provided gene expression data. In particular, our algorithm is based on solving a sequence of mixed integer linear programs and it exhibits better guarantees as well as better runtime performance as compared to the state-of-the-art exact algorithms. Our empirical study in benchmark datasets shows large improvement in terms of computational speed.