JUCS - Journal of Universal Computer Science 12(6): 725-745, doi: 10.3217/jucs-012-06-0725

Improving Deterministic and Randomized Exponential-Time Algorithms for the Satisfiability, the Colorability, and the Domatic Number Problem

‡ Heinrich-Heine-University Düsseldorf, Germany

Corresponding author: Tobias Riege ( riege@cs.uni-duesseldorf.de ) Citation:
Riege T, Rothe J (2006) Improving Deterministic and Randomized Exponential-Time Algorithms for the Satisfiability, the Colorability, and the Domatic Number Problem. JUCS - Journal of Universal Computer Science 12(6): 725-745. https://doi.org/10.3217/jucs-012-06-0725 |

Abstract

NP-complete problems cannot have efficient algorithms unless P = NP. Due to their importance in practice, however, it is useful to improve the known exponential-time algorithms for NP-complete problems. We survey some of the recent results on such improved exponential-time algorithms for the NP-complete problems satisfiability, graph colorability, and the domatic number problem. The deterministic time bounds are compared with the corresponding time bounds of randomized algorithms, which often run faster but only at the cost of having a certain error probability.

Keywords

exact computation, exponential-time algorithms, deterministic algorithms, randomized algorithms