a Department of Computer and Information Science, Linköping University, SE-581 83, Linköping, Sweden
b Department of Computer and Information Sciences, Temple University, 1805 N Broad St Fl 4, Philadelphia, PA 19122, USA
Abstract:
We present four polynomial space and exponential time algorithms for variants of the E
S
problem. First, an O(1.1120n) (where n is the number of variables) time algorithm for the NP-complete decision problem of E
3-S
, and then an O(1.1907n) time algorithm for the general decision problem of E
S
. The best previous algorithms run in O(1.1193n) and O(1.2299n) time, respectively. For the #P-complete problem of counting the number of models for E
3-S
we present an O(1.1487n) time algorithm. We also present an O(1.2190n) time algorithm for the general problem of counting the number of models for E
S
; presenting a simple reduction, we show how this algorithm can be used for computing the permanent of a 0/1 matrix.