A 2O(n1-1/d log n) time algorithm for d-dimensional protein folding in the HP-model

Abstract

The protein folding problem in the HP-model is NP-hard in both 2D and 3D [4,6]. The problem is to put a sequence, consisting of two characters H and P, on a d-dimensional grid to have the maximal number of HH contacts. We design a 2O(n1-1/d log n) time algorithm for d-dimensional protein folding in the HP-model. In particular, our algorithm has O(2 6.145√n log n) and O(24.306n2/3 log n) computational time in 2D and 3D respectively. The algorithm is derived via our separator theorem for points on a d-dimensional grid. For example, for a set of n points P on a 2-dimensional grid, there is a separator with at most 1.129√n points that partitions P into two sides with at most (2/3)n points on each side. Our separator theorem for grid points has a greatly reduced upper bound than that for the general planar graph [2]. © Springer-Verlag Berlin Heidelberg 2004.