Phylogenetic tree reconciliation is widely used in the fields of molecular evolution, cophylogenetics, parasitology, and biogeography to study the evolutionary histories of pairs of entities. In these contexts, reconciliation is often performed using maximum parsimony under the DTL (Duplication-Transfer-Loss) event model. In general, the number of maximum parsimony reconciliations (MPRs) can grow exponentially with the size of the trees. While a number of previous efforts have been made to count the number of MPRs, find representative MPRs, and compute the frequencies of events across the space of MPRs, little is known about the structure of MPR space. In particular, how different are MPRs in terms of the events that they comprise?
Linear programming (LP) is one of the most widely-applied techniques in operations research. Many methods have been developed and several others are being proposed for solving LP problems, including the famous simplex method and interior point algorithms. This study was aimed at introducing a new method for solving LP problems. The proposed algorithm starts from an interior point and then carries out orthogonal projections using parametric straight lines to move between the interior and polyhedron frontier defining the feasible region until reaching the extreme optimal point.
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