Quasiconvex Analysis of Backtracking Algorithms [article]

David Eppstein
2003 arXiv   pre-print
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
more » ... lting 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.
arXiv:cs/0304018v2 fatcat:7zpmbvdaqjg2xpcgadjok2fcg4