Bounds on the minimum mosaic of population sequences under recombination

Abstract

We study the minimum mosaic problem, an optimization problem originated in population genomics. We develop a new lower bound, called the C bound. The C bound is provably higher and significantly more accurate in practice than an existing bound. We show how to compute the exact C bound using integer linear programming. We also show that a weaker version of the C bound is also more accurate than the existing bound, and can be computed in polynomial time. Simulation shows that the new bounds often match the exact optimum at least for the range of data we tested. Moreover, we give an analytical upper bound for the minimum mosaic problem. © Springer-Verlag Berlin Heidelberg 2010.