Abstract
We study the complexity of local search for the Boolean constraint satisfaction problem (CSP), in the following form: given a CSP instance, that is, a collection of constraints, and a solution to it, the question is whether there is a better (lighter, i.e., having strictly less Hamming weight) solution within a given distance from the initial solution. We classify the complexity, both classical and parameterized, of such problems by a Schaefer-style dichotomy result, that is, with a restricted set of allowed types of constraints. Our results show that there is a considerable amount of such problems that are NP-hard, but fixed-parameter tractable when parameterized by the distance.
The first author is supported by UK EPSRC grants EP/C543831/1 and EP/C54384X/1; the second author is supported by the Magyary Zoltán Felsőoktatási Közalapítvány and the Hungarian National Research Fund (OTKA grant 67651).
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
Chapdelaine, P., Creignou, N.: The complexity of Boolean constraint satisfaction local search problems. Annals of Mathematics and Artificial Intelligence 43, 51–63 (2005)
Cohen, D., Jeavons, P.: The complexity of constraint languages. In: Rossi, F., van Beek, P., Walsh, T. (eds.) Handbook of Constraint Programming, ch. 8. Elsevier, Amsterdam (2006)
Creignou, N., Khanna, S., Sudan, M.: Complexity Classifications of Boolean Constraint Satisfaction Problems. SIAM Monographs on Discrete Mathematics and Applications, vol. 7 (2001)
Crescenzi, P., Rossi, G.: On the Hamming distance of constraint satisfaction problems. Theoretical Computer Science 288(1), 85–100 (2002)
Dantsin, E., Goerdt, A., Hirsch, E., Kannan, R., Kleinberg, J., Papadimitriou, C., Raghavan, P., Schöning, U.: A deterministic \((2-\frac{2}{k+1})^n\) algorithm for k-SAT based on local search. Theoretical Computer Science 289, 69–83 (2002)
Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)
Fellows, M.R.: Parameterized complexity: new developments and research frontiers. In: Aspects of Complexity (Kaikura, 2000). de Gruyter Series in Logic and Applications, vol. 4, pp. 51–72 (2001)
Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006)
Gu, J., Purdom, P., Franko, J., Wah, B.W.: Algorithms for the Satisfiability Problem. Cambridge University Press, Cambridge (2000)
Hirsch, E.: SAT local search algorithms: worst-case study. Journal of Automated Reasoning 24, 127–143 (2000)
Hoos, H., Tsang, E.: Local search methods. In: Rossi, F., van Beek, P., Walsh, T. (eds.) Handbook of Constraint Programming. ch. 5. Elsevier, Amsterdam (2006)
Kirousis, L., Kolaitis, P.: The complexity of minimal satisfiability problems. Information and Computation 187, 20–39 (2003)
Marx, D.: Parameterized complexity of constraint satisfaction problems. Computational Complexity 14, 153–183 (2005)
Marx, D.: Searching the k-change neighborhood for TSP is W[1]-hard. Operations Research Letters 36, 31–36 (2008)
Schaefer, T.J.: The complexity of satisfiability problems. In: STOC 1978, pp. 216–226 (1978)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Krokhin, A., Marx, D. (2008). On the Hardness of Losing Weight. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds) Automata, Languages and Programming. ICALP 2008. Lecture Notes in Computer Science, vol 5125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70575-8_54
Download citation
DOI: https://doi.org/10.1007/978-3-540-70575-8_54
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70574-1
Online ISBN: 978-3-540-70575-8
eBook Packages: Computer ScienceComputer Science (R0)