Quasiconvex Analysis of Backtracking Algorithms
摘要
We consider a class of multivariate recurrences frequently arising in the worst case analysis of Davis-Putnam-style exponential time backtracking algorithms for NP-hard problems. We describe a technique for proving asymptotic upper bounds on these recurrences, by using a suitable weight function to reduce the problem to that of solving univariate linear recurrences; show how to use quasiconvex programming to determine the weight function yielding the smallest upper bound; and prove that the resulting upper bounds are within a polynomial factor of the true asymptotics of the recurrence. We develop and implement a multiple-gradient descent algorithm for the resulting quasiconvex programs, using a real-number arithmetic package for guaranteed accuracy of the computed worst case time bounds.
引用
@article{arxiv.cs/0304018,
title = {Quasiconvex Analysis of Backtracking Algorithms},
author = {David Eppstein},
journal= {arXiv preprint arXiv:cs/0304018},
year = {2007}
}
备注
12 pages, 2 figures. This revision includes a larger example recurrence and reports on a second implementation of the algorithm