The Complexity of the Distributed Constraint Satisfaction Problem

Journal article

AbstractWe study the complexity of the Distributed Constraint Satisfaction Problem (DCSP) on a synchronous, anonymous network from a theoretical standpoint. In this setting, variables and constraints are controlled by agents which communicate with each other by sending messages through fixed communication channels. Our results endorse the well-known fact from classical CSPs that the complexity of fixed-template computational problems depends on the template’s invariance under certain operations. Specifically, we show that DCSP(Γ) is polynomial-time tractable if and only if Γ is invariant under symmetric polymorphisms of all arities. Otherwise, there are no algorithms that solve DCSP(Γ) in finite time. We also show that the same condition holds for the search variant of DCSP. Collaterally, our results unveil a feature of the processes’ neighbourhood in a distributed network, its iterated degree, which plays a major role in the analysis. We explore this notion establishing a tight connection with the basic linear programming relaxation of a CSP.

Authors: Butti, S; Dalmau, V

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Theory of Computing Systems
• Volume: 68
• Issue: 4
• Pages: 838-867
• Publication date: 2022-07-08
• DOI: 10.1007/s00224-022-10091-y
• EISSN: 1433-0490
• ISSN: 1432-4350
• Language: English
• Keywords: Algorithm; Mathematical optimization; Computer science; Artificial intelligence; Computational complexity theory; Time complexity; Constraint (computer-aided design); Theoretical computer science; Mathematics; Iterated function; Constraint satisfaction dual problem; Constraint logic programming; Constraint satisfaction problem; Constraint satisfaction