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Detecting Phylogenetic Footprint Clusters by Optimizing Barbeques
Axel Mosig, Türker Biyikoglu, Sonja J. Prohaska and Peter F. Stadler
Taking a geometric view on a problem occurring in the context of phylogenetic footprinting, we study the so-called Best Barbeque Problem. The Best Barbeque Problem asks for simultaneously stabbing a maximum number of differently colored intervals from $K$ arrangements of colored intervals. This geometric problem leads to a combinatorial optimization problem, a decision version of which is shown to be NP-complete. Due to its relevance in biological applications, we propose two branch-and-bound algorithms to detect footprint clusters in some real world instances of phylogenetic footprints. Finally, we point out other geometric and combinatorial scenarios where optimizing barbeques might be of practical relevance.