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

Maurice Queyranne () and Laurence A. Wolsey
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Maurice Queyranne: University of British Columbia
Laurence A. Wolsey: Université catholique de Louvain

Journal of Combinatorial Optimization, 2018, vol. 36, issue 1, No 9, 90-107

Abstract: 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.

Keywords: Shortest paths; Turn restrictions; Convex polygons; Convex subsets; Extended formulation; Dynamic programming (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10878-018-0281-y

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