An efficient fixed-parameter algorithm for 3-Hitting Set

Backdoor Sets of Quantified Boolean Formulas

“…Currently, the fastest known fixed-parameter algorithm for the former problem is due to Chen, Kanj, and Xia [7] and runs in time O(1.2738 k + kn). The fastest known fixed-parameter algorithm for the latter problem is due to Niedermeier and Rossmanith [21] and runs in time O(2.270 k + n); an alternative algorithm is due to Abu-Khzam [1]. If no hitting set of size at most k is found, then we know by Lemmas 3 and 4 that F has no strong C-backdoor set of size at most k, and we can reject the instance.…”

A Gentle Introduction to Memetic Algorithms

“…Recently, Niedermeier and Rossmanith have presented an algorithm that solves this problem in time O(2.311 k + n) [165]. We leave as an exercise to the reader the task of finding recombination operators that take advantage of this algorithm.…”

Backdoor Sets of Quantified Boolean Formulas

“…The algorithms take into account variable dependencies that are provided as additional input (below we will address the problem of computing the dependencies). Our algorithms make use of known fixed-parameter algorithms for vertex cover and hitting set [7,21]. Once a strong backdoor set is found, the formula can be evaluated by considering all truth assignments to the variables in the backdoor set.…”

“…The fastest known fixed-parameter algorithm for the latter problem is due to Niedermeier and Rossmanith [21] and runs in time O(2.270 k + n); an alternative algorithm is due to Abu-Khzam [1]. If no hitting set of size at most k is found, then we know by Lemmas 3 and 4 that F has no strong C-backdoor set of size at most k, and we can reject the instance.…”