The Complexity of Making Unique Choices: Approximating 1-in-k SAT
We study the approximability of 1-in-kSAT, the variant of Max kSAT where a clause is deemed satisfied when precisely one of its literals is satisfied. We also investigate different special cases of the problem, including those obtained by restricting the literals to be unnegated and/or all clauses to have size exactly k. Our results show that the 1-in-kSAT problem exhibits some rather peculiar phenomena in the realm of constraint satisfaction problems. Specifically, the problem becomes substantially easier to approximate with perfect completeness as well as when negations of literals are not allowed.
KeywordsApproximation Algorithm Polynomial Time Random Assignment Constraint Satisfaction Problem Boolean Variable
Unable to display preview. Download preview PDF.
- 2.Chlebus, B.S., Gasieniec, L., Gibbons, A., Pelc, A., Rytter, W.: Deterministic broadcasting in unknown radio networks. In: Proceedings of the 11th ACM-SIAM Symposium on Discrete Algorithms, pp. 861–870 (2000)Google Scholar
- 4.Demaine, E., Feige, U., Hajiaghayi, M., Salavatipour, M.: Combination can be hard: approximability of the unique coverage problem (April 2005) (manuscript)Google Scholar
- 6.Guruswami, V.: Query-efficient checking of proofs and improved PCP characterizations of NP. Master’s thesis, MIT (1999)Google Scholar
- 7.Guruswami, V., Hartline, J., Karlin, A., Kempe, D., Kenyon, C., McSherry, F.: On profit-maximizing envy-free pricing. In: Proceedings of the 16th ACM-SIAM Symposium on Discrete Algorithms (SODA) (January 2005)Google Scholar
- 8.Samorodnitsky, A., Trevisan, L.: A PCP characterization of NP with optimal amortized query complexity. In: Proceedings of the 32nd ACM Symposium on Theory of Computing (2000)Google Scholar
- 9.Schaefer, T.J.: The complexity of satisfiability problems. In: Proceedings of the 10th ACM Symposium on Theory of Computing, pp. 216–226 (1978)Google Scholar