On a linear program for minimum-weight triangulation

ABSTRACT∗ Arman Yousefi† Neal E. Young‡ Minimum-weight triangulation (MWT) is NP-hard. It has a polynomial-time constant-factor approximation algorithm, and a variety of effective polynomialtime 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.

• Type: Journal
• Year: 2012
• Where: SODA
• Authors: Arman Yousefi, Neal E. Young
• Keywords: Algorithms, Approximation Algorithm, Lp Formulation, Polynomial Time, SODA 2012