Publication details
Backdoor Treewidth for SAT
| Authors | |
|---|---|
| Year of publication | 2017 |
| Type | Article in Proceedings |
| Conference | Theory and Applications of Satisfiability Testing - SAT 2017 - 20th International Conference, Melbourne, VIC, Australia, August 28 - September 1, 2017, Proceedings |
| MU Faculty or unit | |
| Citation | |
| Web | https://link.springer.com/chapter/10.1007/978-3-319-66263-3_2 |
| Doi | http://dx.doi.org/10.1007/978-3-319-66263-3_2 |
| Keywords | Treewidth; Parameterized Complexity; SAT; Backdoors |
| Description | A strong backdoor in a CNF formula is a set of variables such that each possible instantiation of these variables moves the formula into a tractable class. The algorithmic problem of finding a strong backdoor has been the subject of intensive study, mostly within the parameterized complexity framework. Results to date focused primarily on backdoors of small size. In this paper we propose a new approach for algorithmically exploiting strong backdoors for SAT: instead of focusing on small backdoors, we focus on backdoors with certain structural properties. In particular, we consider backdoors that have a certain tree-like structure, formally captured by the notion of backdoor treewidth. First, we provide a fixed-parameter algorithm for SAT parameterized by the backdoor treewidth w.r.t. the fundamental tractable classes Horn, Anti-Horn, and 2CNF. Second, we consider the more general setting where the backdoor decomposes the instance into components belonging to different tractable classes, albeit focusing on backdoors of treewidth 1 (i.e., acyclic backdoors). We give polynomial-time algorithms for SAT and #SAT for instances that admit such an acyclic backdoor. |