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arXiv · 1111.5305

On a Linear Program for Minimum-Weight Triangulation

Arman Yousefi·Neal E. Young
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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.

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Arman Yousefi, Neal E. Young. 2011-11-22. On a Linear Program for Minimum-Weight Triangulation. https://doi.org/10.1137/120887928

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