On a linear program for minimum-weight triangulation

Authors:
Arman Yousefi;Neal E. Young
Affiliations:
-;University of California, Riverside
Venue:
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Year:
2012

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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.