A Lower Bound for the Breakpoint Phylogeny Problem

Abstract

Breakpoint phylogenies methods have been shown to be an effective way to extract phylogenetic information from gene order data. Currently, the only practical breakpoint phylogeny algorithms for the analysis of large genomes with varied gene content are heuristics with no optimality guarantee. Here we address this shortcoming by describing new bounds for the breakpoint median problem, and for the more complicated breakpoint phylogeny problem. In both cases we employ Lagrangian multipliers and subgradient optimization to tighten the bounds. The experimental results are promising: we achieve lower bounds close to the upper bounds established using breakpoint phylogeny heuristics.KeywordsTravel Salesman ProblemTravel Salesman ProblemSteiner PointBreakpoint DistanceSubgradient OptimizationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.