The complexity of global cardinality constraints
Andrei A. Bulatov (Simon Fraser University), Daniel Marx (Tel Aviv, University)
TL;DR
This paper characterizes the computational complexity of CSPs with global cardinality constraints, identifying which are solvable in polynomial time and which are NP-complete based on the set of allowed relations.
Contribution
It provides a complete classification of the complexity of CCSP(G) problems depending on the set G of relations, highlighting the boundary between tractable and NP-complete cases.
Findings
Polynomial-time solvable for certain relation sets G
NP-complete for other relation sets G
Complete complexity classification of CCSP(G) problems
Abstract
In a constraint satisfaction problem (CSP) the goal is to find an assignment of a given set of variables subject to specified constraints. A global cardinality constraint is an additional requirement that prescribes how many variables must be assigned a certain value. We study the complexity of the problem CCSP(G), the constraint satisfaction problem with global cardinality constraints that allows only relations from the set G. The main result of this paper characterizes sets G that give rise to problems solvable in polynomial time, and states that the remaining such problems are NP-complete.
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