Optimally Separating Sequences

Abstract

We consider the problem of separating two distinct classes of k similar sequences of length n over an alphabet of size s that have been optimally multi-aligned. An objective function based on minimizing the consensus score of the separated halves is introduced and we present an O (k³n) heuristic algorithm and two optimal branch-and-bound algorithms for the problem. The branchand-bound algorithms involve progressively more powerful lower bound functions for pruning the O (2^k) search tree. The simpler lower bound takes O (n) time to evaluate given O (sn) global data structures and the stronger bound takes O ((k+s) n) time by virtue of an efficient solution to the problem of finding the second-maximum envelope of a set of piece-wise affine curves. In a series of empirical trials we establish the degree to which classes can be separated using our metric and the effective pruning efficiency of the two branch-and-bound algorithms.