Abstract
In a discussion on the computational complexity of approximately solving Boolean counting constraint satisfaction problems (or #CSPs), we demonstrate the approximability of two constant unary constraints by an arbitrary nonempty set of real-valued constraints. A use of auxiliary free unary constraints has proven to be useful in establishing a complete classification of weighted #CSPs. Using our approximability result, we can clarify the role of such auxiliary free unary constraints by constructing approximation-preserving reductions from #SAT to #CSPs with symmetric real-valued constraints of arbitrary arities.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cai, J., Lu, P.: Holographic algorithms: from arts to science. J. Comput. System Sci. 77, 41–61 (2011)
Cai, J., Lu, P., Xia, M.: Holant problems and counting CSP. In: STOC 2009, pp. 715–724 (2009)
Creignou, N.: A dichotomy theorem for maximum generalized satisfiability problems. J. Comput. System Sci. 51, 511–522 (1995)
Creignou, N., Hermann, M.: Complexity of generalized satisfiability counting problems. Inform. Comput. 125, 1–12 (1996)
Dalmau, V., Ford, D.K.: Generalized Satisfiability with Limited Occurrences per Variable: A Study through Delta-Matroid Parity. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 358–367. Springer, Heidelberg (2003)
Dyer, M., Goldberg, L.A., Greenhill, C., Jerrum, M.: The relative complexity of approximating counting problems. Algorithmica 38, 471–500 (2004)
Dyer, M., Goldberg, L.A., Jerrum, M.: The complexity of weighted Boolean #CSP. SIAM J. Comput. 38, 1970–1986 (2009)
Dyer, M., Goldberg, L.A., Jerrum, M.: An approximation trichotomy for Boolean #CSP. J. Comput. System Sci. 76, 267–277 (2010)
Schaefer, T.J.: The complexity of satisfiability problems. In: STOC 1978, pp. 216–226 (1978)
Yamakami, T.: Approximate counting for complex-weighted Boolean constraint satisfaction problems. Inform. Comput. 219, 17–38 (2012)
Yamakami, T.: A dichotomy theorem for the approximation complexity of complex-weighted bounded-degree Boolean #CSPs. Thoer. Comput. Sci. 447, 120–135 (2012)
Yamakami, T.: Optimization, Randomized Approximability, and Boolean Constraint Satisfaction Problems. In: Asano, T., Nakano, S.-i., Okamoto, Y., Watanabe, O. (eds.) ISAAC 2011. LNCS, vol. 7074, pp. 454–463. Springer, Heidelberg (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yamakami, T. (2012). Constant Unary Constraints and Symmetric Real-Weighted Counting CSPs. In: Chao, KM., Hsu, Ts., Lee, DT. (eds) Algorithms and Computation. ISAAC 2012. Lecture Notes in Computer Science, vol 7676. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35261-4_27
Download citation
DOI: https://doi.org/10.1007/978-3-642-35261-4_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35260-7
Online ISBN: 978-3-642-35261-4
eBook Packages: Computer ScienceComputer Science (R0)