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

Optimum turn-restricted paths, nested compatibility, and optimum convex polygons 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Combinatorial Optimization Springer Journals

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

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Combinatorics; Convex and Discrete Geometry; Mathematical Modeling and Industrial Mathematics; Theory of Computation; Optimization; Operations Research/Decision Theory
ISSN
1382-6905
eISSN
1573-2886
D.O.I.
10.1007/s10878-018-0281-y
Publisher site
See Article on Publisher Site

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.

Journal

Journal of Combinatorial OptimizationSpringer Journals

Published: Apr 5, 2018

References

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