eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2013-02-26
148
159
10.4230/LIPIcs.STACS.2013.148
article
The complexity of approximating conservative counting CSPs
Chen, Xi
Dyer, Martin
Goldberg, Leslie Ann
Jerrum, Mark
Lu, Pinyan
McQuillan, Colin
Richerby, David
We study the complexity of approximation for a weighted counting constraint satisfaction problem #CSP(F). In the conservative case, where F contains all unary functions, a classification is known for the Boolean domain. We give a classification for problems with general finite domain. We define weak log-modularity and weak log-supermodularity, and show that #CSP(F) is in FP if F is weakly log-modular. Otherwise, it is at least as hard to approximate as #BIS, counting independent sets in bipartite graphs, which is believed to be intractable. We further sub-divide the #BIS-hard case. If F is weakly log-supermodular, we show that #CSP(F) is as easy as Boolean log-supermodular weighted #CSP. Otherwise, it is NP-hard to approximate. Finally, we give a trichotomy for the arity-2 case.
Then, #CSP(F) is in FP, is #BIS-equivalent, or is equivalent to #SAT, the problem of approximately counting satisfying assignments of a CNF Boolean formula.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol020-stacs2013/LIPIcs.STACS.2013.148/LIPIcs.STACS.2013.148.pdf
counting constraint satisfaction problem
approximation
complexity