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Modeling and Optimization: Theory and Applications

MOPTA 2016: Modeling and Optimization: Theory and Applications pp 39–53Cite as

Column Generation Approach to the Convex Recoloring Problem on a Tree

Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS,volume 213)

Abstract

The convex recoloring (CR) problem is to recolor the nodes of a colored graph at minimum number of color changes such that each color induces a connected subgraph. We adjust to the convex recoloring problem the column generation framework developed by Johnson et al. (Math Program 62:133–151, 1993). For the convex recoloring problem on a tree, the subproblem to generate columns can be solved in polynomial time by a dynamic programming algorithm. The column generation framework solves the convex recoloring problem on a tree with a large number of colors extremely fast.

Keywords

  • Convex recoloring problem
  • Phylogenetic tree
  • Bioinformatics
  • Clustering problem
  • Column generation
  • Linear programming
  • Large scale optimization
  • Set partition problem

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Author information

Authors and Affiliations

  1. Kellogg School of Management, Northwestern University, Evanston, IL, 60208, USA

    Sunil Chopra

  2. Department of Engineering, Robert Morris University, Moon Twp, PA, 15090, USA

    Ergin Erdem & Sangho Shim

  3. KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon, 34141, Republic of Korea

    Eunseok Kim

Authors
  1. Sunil Chopra
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  2. Ergin Erdem
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  3. Eunseok Kim
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  4. Sangho Shim
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Corresponding author

Correspondence to Sangho Shim .

Editor information

Editors and Affiliations

  1. Industrial and Systems Engineering Department, Lehigh University, Bethlehem, Pennsylvania, USA

    Martin Takáč

  2. Industrial and Systems Engineering Department, Lehigh University, Bethlehem, Pennsylvania, USA

    Tamás Terlaky

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Chopra, S., Erdem, E., Kim, E., Shim, S. (2017). Column Generation Approach to the Convex Recoloring Problem on a Tree. In: Takáč, M., Terlaky, T. (eds) Modeling and Optimization: Theory and Applications. MOPTA 2016. Springer Proceedings in Mathematics & Statistics, vol 213. Springer, Cham. https://doi.org/10.1007/978-3-319-66616-7_3

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