Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
The complexity of homomorphism and constraint satisfaction problems seen from the other side
Journal of the ACM (JACM)
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Complexity and algorithms for well-structured k-SAT instances
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
Some remarks on the incompressibility of width-parameterized SAT instances
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
| Hi-index | 0.89 |
We characterize the complexity of SAT instances with path-decompositions of width w(n). Although pathwidth is the most restrictive among the studied width-parameterizations of SAT, the most time-efficient algorithms known for such SAT instances run in time 2^@W^(^w^(^n^)^), even when the path-decomposition is given in the input. We wish to better understand the decision complexity of SAT instances of width @w(logn). We provide an exact correspondence between SAT"p"w[w(n)], the problem of SAT instances with given path decomposition of width w(n), and NL[r(n)], the class of problems decided by logspace Turing Machines with at most r(n) passes over the nondeterministic tape. In particular, we show that SAT"p"w[w(n)] is hard for NL[w(n)logn] under log-space reductions. When NL[w(n)logn] is closed under logspace reductions, which is the case for the most interesting w(n)'s, we show that SAT"p"w[w(n)] is also complete.