Lower Bounds for Maximum Parsimony with Gene Order Data

Abstract. In this paper, we study lower bound techniques for branchand-bound algorithms for maximum parsimony, with a focus on gene order data. We give a simple O(n3 ) time dynamic programming algorithm for computing the maximum circular ordering lower bound. The well-known gene order phylogeny program, GRAPPA, currently implements the brute-force exponential time algorithm and the Swap-as-yougo heuristic. Our experiments show a significant improvement over both these methods in practice. Next, we show that the linear programmingbased lower bound of Tang and Moret can be greatly simplified, allowing us to solve the LP very efficiently. Finally, we formalize the problem of computing the circular ordering lower bound, when the tree topologies are generated bottom-up, as a Path-Constrained Travelling Salesman Problem, and give a 3-approximation algorithm for it. This is a special case of the more general Precedence-Constrained Travelling Salesman Problem and has not previously been studie...

• Type: Conference
• Year: 2005
• Where: RECOMB
• Authors: Abraham Bachrach, Kevin Chen, Chris Harrelson, Radu Mihaescu, Satish Rao, Apurva Shah
• Keywords: Computational Biology, Lower Bound, Ordering Lower Bound, RECOMB 2005, Travelling Salesman Problem