Rounding semidefinite programs for large-domain problems via Brownian motion
Data Structures and Algorithms
2018-12-11 v1
Abstract
We present a new simple method for rounding a semidefinite programming relaxation of a constraint satisfaction problem. We apply it to the problem of approximate angular synchronization. Specifically, we are given directed distances on a circle (i.e., directed angles) between pairs of elements and our goal is to assign the elements to positions on a circle so as to preserve these distances as much as possible. The feasibility of our rounding scheme is based on properties of the well-known stochastic process called Brownian motion. Based on computational and other evidence, we conjecture that this rounding scheme yields an approximation guarantee that is very close to the best-possible guarantee (assuming the Unique-Games Conjecture).
Cite
@article{arxiv.1812.03572,
title = {Rounding semidefinite programs for large-domain problems via Brownian motion},
author = {Kevin L. Chang and Alantha Newman},
journal= {arXiv preprint arXiv:1812.03572},
year = {2018}
}