An extended formulation of the convex recoloring problem on a tree

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dc.contributor.author Chopra, Sunil
dc.contributor.author Filipecki, Bartosz
dc.contributor.author Lee, Kangbok
dc.contributor.author Ryu, Minseok
dc.contributor.author Shim, Sang Ho
dc.contributor.author Vyve, Mathieu Van
dc.date.accessioned 2020-02-10T15:40:59Z
dc.date.available 2020-02-10T15:40:59Z
dc.date.issued 2017
dc.identifier.citation Chopra, S., Filipecki, B., Lee, K. et al. Math. Program. (2017) 165: 529. https://doi.org/10.1007/s10107-016-1094-3 en_US
dc.identifier.uri http://hdl.handle.net/11347/349
dc.description.abstract We introduce a strong extended formulation of the convex recoloring problem on a tree, which has an application in analyzing phylogenetic trees. The extended formulation has only a polynomial number of constraints, but dominates the conventional formulation and the exponentially many valid inequalities introduced by Campêlo et al. (Math Progr 156:303–330, 2016). We show that all valid inequalities introduced by Campêlo et al. can be derived from the extended formulation. We also show that the natural restriction of the extended formulation provides a complete inequality description of the polytope of subtrees of a tree. The solution time using the extended formulation is much smaller than that with the conventional formulation. Moreover the extended formulation solves all the problem instances attempted in Campêlo et al. (2016) and larger sized instances at the root node of the branch-and-bound tree without branching. en_US
dc.language.iso en_US en_US
dc.publisher Mathematical Programming en_US
dc.subject convex recoloring en_US
dc.subject polytope of subtrees en_US
dc.subject Formulation en_US
dc.title An extended formulation of the convex recoloring problem on a tree en_US
dc.type Article en_US


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