Confronting hardness using a hybrid approach

Virginia Vassilevska, Ryan Williams, Shan Leung Maverick Woo
2006 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06  
A hybrid algorithm is a collection of heuristics, paired with a polynomial time selector S that runs on the input to decide which heuristic should be executed to solve the problem. Hybrid algorithms are of particular interest in scenarios where the selector must decide between heuristics that are "good" with respect to different complexity measures. We focus on hybrid algorithms with a "hardnessdefying" property: for a problem Π, there is a set of complexity measures {m i } whereby Π is known
more » ... conjectured to be unsolvable for each m i , but for each heuristic h i of the hybrid algorithm, one can give a complexity guarantee for h i on the instances of Π that S selects for h i that is strictly better than m i . More concretely, we show that for several NP-hard problems, a given instance can either be solved exactly with substantially improved runtime (e.g. 2 o(n) ), or be approximated in polynomial time with an approximation ratio exceeding that of the known or conjectured inapproximability of the problem, assuming P = NP.
doi:10.1145/1109557.1109558 fatcat:4g2juiedlbgbxjodluo5v6rwo4