Upper and lower bounds for weak backdoor set detection

Abstract

We obtain upper and lower bounds for running times of exponential time algorithms for the detection of weak backdoor sets of 3CNF formulas, considering various base classes. These results include (omitting polynomial factors), (i) a 4.54k algorithm to detect whether there is a weak backdoor set of at most k variables into the class of Horn formulas; (ii) a 2.27k algorithm to detect whether there is a weak backdoor set of at most k variables into the class of Krom formulas. These bounds improve an earlier known bound of 6k. We also prove a 2k lower bound for these problems, subject to the Strong Exponential Time Hypothesis. © 2013 Springer-Verlag.