Approximating partition functions of bounded-degree Boolean counting Constraint Satisfaction Problems
نویسندگان
چکیده
We study the complexity of # CSP Δ ( Γ ) , which is problem counting satisfying assignments to instances with constraints from and whose variables can appear at most times. Our main result shows that: (i) if every function in affine, then FP for all Δ, (ii) otherwise, a class called I M 2 large equivalent under approximation-preserving reductions independent sets bipartite graphs, (iii) it NP -hard approximate even within an exponential factor.
منابع مشابه
Approximating Partition Functions of Bounded-Degree Boolean Counting Constraint Satisfaction Problems
We study the complexity of approximate counting Constraint Satisfaction Problems (#CSPs) in a bounded degree setting. Specifically, given a Boolean constraint language Γ and a degree bound ∆, we study the complexity of #CSP∆(Γ), which is the problem of counting satisfying assignments to CSP instances with constraints from Γ and whose variables can appear at most ∆ times. Our main result shows t...
متن کاملApproximate Counting for Complex-Weighted Boolean Constraint Satisfaction Problems
Constraint satisfaction problems (or CSPs) have been extensively studied in, for instance, artificial intelligence, database theory, graph theory, and statistical physics. From a practical viewpoint, it is beneficial to approximately solve CSPs. When one tries to approximate the total number of truth assignments that satisfy all Boolean constraints for (unweighted) Boolean CSPs, there is a know...
متن کاملCounting Constraint Satisfaction Problems
This chapter surveys counting Constraint Satisfaction Problems (counting CSPs, or #CSPs) and their computational complexity. It aims to provide an introduction to the main concepts and techniques, and present a representative selection of results and open problems. It does not cover holants, which are the subject of a separate chapter. 1998 ACM Subject Classification F.2.2 Nonnumerical Algorith...
متن کاملOn the Bounded Degree Restriction of Constraint Satisfaction Problems
Given a graph H, let b(H) be the minimum integer b, if it exists, for which H-colouring is NP -complete when restricted to instances with degree bounded by b. We show for any loopless non-bipartite graphs H that b(H) is bounded above by a function of the size of H. Futhermore, we get tight upper bounds on b(H) for various H. For example, we show that b(H) = 3 for any graph H with girth at least...
متن کاملThe Complexity of Approximating Bounded-Degree Boolean \sharp CSP
The degree of a CSP instance is the maximum number of times that a variable may appear in the scope of constraints. We consider the approximate counting problem for Boolean CSPs with bounded-degree instances for constraint languages containing the two unary constant relations {0} and {1}. When the maximum degree is at least 25 we obtain a complete classification of the complexity of this proble...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 2021
ISSN: ['1090-2724', '0022-0000']
DOI: https://doi.org/10.1016/j.jcss.2020.08.003