Solvingd-SAT via Backdoors to Small Treewidth [chapter]

Fedor V. Fomin, Daniel Lokshtanov, Neeldhara Misra, M. S. Ramanujan, Saket Saurabh
2014 Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms  
One of our main technical contributions is a linear time "protrusion replacer" improving over a O(n log 2 n)-time procedure of Fomin et al. (FOCS 2012). The new deterministic linear time protrusion replacer has several applications in kernelization and parameterized algorithms. At first glance, the problem of detecting a weak W ηbackdoor set resembles the algorithmic graph problem of deleting at most k vertices such that the new graph is of treewidth at most t. However, as it was observed by
more » ... pers and Szeider in [14], already the problem of computing a weak backdoor set to acyclic d-SAT is very different from the seemingly related Feedback Vertex Set problem because while the size of the backdoor, k, can be very small, the treewidth of the incidence graph can be unbounded by any function of k. As a result, the techniques developed by a subset of the authors in 631
doi:10.1137/1.9781611973730.43 dblp:conf/soda/FominLMRS15 fatcat:4hppsxbm3feybggwnxhjnxv2fq