On a Linear Program for Minimum-Weight Triangulation
Computational Geometry
2015-06-02 v2 Data Structures and Algorithms
Abstract
Minimum-weight triangulation (MWT) is NP-hard. It has a polynomial-time constant-factor approximation algorithm, and a variety of effective polynomial- time heuristics that, for many instances, can find the exact MWT. Linear programs (LPs) for MWT are well-studied, but previously no connection was known between any LP and any approximation algorithm or heuristic for MWT. Here we show the first such connections: for an LP formulation due to Dantzig et al. (1985): (i) the integrality gap is bounded by a constant; (ii) given any instance, if the aforementioned heuristics find the MWT, then so does the LP.
Cite
@article{arxiv.1111.5305,
title = {On a Linear Program for Minimum-Weight Triangulation},
author = {Arman Yousefi and Neal E. Young},
journal= {arXiv preprint arXiv:1111.5305},
year = {2015}
}
Comments
To appear in SICOMP. Extended abstract appeared in SODA 2012