A robust model for finding optimal evolutionary trees
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Erratum: the Travelling Salesman and the Pq-Tree
Mathematics of Operations Research
Constrained TSP and Low-Power Computing
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
GESTALT: Genomic Steiner Alignments
CPM '99 Proceedings of the 10th Annual Symposium on Combinatorial Pattern Matching
Sequential and Parallel Algorithms for Mixed Packing and Covering
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Large-scale phylogenetic reconstruction from arbitrary gene-order data
Large-scale phylogenetic reconstruction from arbitrary gene-order data
Linear programming for phylogenetic reconstruction based on gene rearrangements
CPM'05 Proceedings of the 16th annual conference on Combinatorial Pattern Matching
An O(log n) approximation ratio for the asymmetric traveling salesman path problem
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
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In this paper, we study lower bound techniques for branch-and-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, where n is the number of leaves. The well-known gene order phylogeny program, GRAPPA, currently implements two heuristic approximations to this lower bounds. Our experiments show a significant improvement over both these methods in practice. Next, we show that the linear programming-based lower bound of Tang and Moret (Tang and Moret, 2005) can be greatly simplified, allowing us to solve the LP in O*n3) time in the worst case, and in O*(n2.5) time amortized over all binary trees. Finally, we formalize the problem of computing the circular ordering lower bound, when the tree topologies are generated bottom-up, as a Path-Constrained Traveling Salesman Problem, and give a polynomial-time 3-approximation algorithm for it. This is a special case of the more general Precedence-Constrained Travelling Salesman Problem and has not previously been studied, to the best of our knowledge.