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Optimum turn-restricted paths, nested compatibility, and optimum convex polygons

Author

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  • Maurice Queyranne

    (University of British Columbia)

  • Laurence A. Wolsey

    (Université catholique de Louvain)

Abstract

We consider two apparently unrelated classes of combinatorial and geometric optimization problems. First, we give compact extended formulations, i.e., polynomial-size linear programming formulations with integer optima, for optimum path problems with turn restrictions satisfying a nested compatibility condition in acyclic digraphs. We then apply these results to optimum convex polygon problems in the plane, by interpreting certain dynamic programming algorithms as sequences of optimum turn-restricted path problems with nested compatibility in acyclic digraphs. As a result, we derive compact extended formulations for these geometric problems as well.

Suggested Citation

  • Maurice Queyranne & Laurence A. Wolsey, 2018. "Optimum turn-restricted paths, nested compatibility, and optimum convex polygons," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 90-107, July.
  • Handle: RePEc:spr:jcomop:v:36:y:2018:i:1:d:10.1007_s10878-018-0281-y
    DOI: 10.1007/s10878-018-0281-y
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    References listed on IDEAS

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    1. Eliécer Gutiérrez & Andrés Medaglia, 2008. "Labeling algorithm for the shortest path problem with turn prohibitions with application to large-scale road networks," Annals of Operations Research, Springer, vol. 157(1), pages 169-182, January.
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