In this paper, we propose a comprehensive study of second-order consistencies (i.e., consistencies identifying inconsistent pairs of values) for constraint satisfaction. We build a full picture of the relationships existing between four basic second-order consistencies, namely path consistency (PC), 3-consistency (3C), dual consistency (DC) and 2-singleton arc consistency (2SAC), as well as their conservative and strong variants. Interestingly, dual consistency is an original property that can be established by using the outcome of the enforcement of generalized arc consistency (GAC), which makes it rather easy to obtain since constraint solvers typically maintain GAC during search. On binary constraint networks, DC is equivalent to PC, but its restriction to existing constraints, called conservative dual consistency (CDC), is strictly stronger than traditional conservative consistencies derived from path consistency, namely partial path consistency (PPC) and conservative path consistency (CPC). After introducing a general algorithm to enforce strong (C)DC, we present the results of an experimentation over a wide range of benchmarks that demonstrate the interest of (conservative) dual consistency. In particular, we show that enforcing (C)DC before search clearly improves the performance of MAC (the algorithm that maintains GAC during search) on several binary and non-binary structured problems

The Constraint Satisfaction Problem (CSP) formalism is used to represent many combinatorial decision problems instances simply and efficiently. However, many such problems cannot be solved on a single, centralized computer for various reasons (e.g., their excessive size or privacy). The Distributed CSP (DisCSP) extends the CSP model to allow such combinatorial decision problems to be modelled and handled. In this paper, we propose a complete DisCSP-solving algorithm, called Distributed Backtracking with Sessions (DBS), which can solve DisCSP so that each agent encapsulates a whole "complex" problem with many variables and constraints. We prove that the algorithm is sound and complete, and generates promising experimental results.

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Privacy has traditionally been a major motivation for decentralized problem solving. However, even though several metrics have been proposed to quantify it, none of them is easily integrated with common solvers. Constraint programming is a fundamental paradigm used to approach various families of problems. We introduce Utilitarian Distributed Constraint Satisfaction Problems (UDisCSP) where the utility of each state is estimated as the difference between the the expected rewards for agreements on assignments for shared variables, and the expected cost of privacy loss.Therefore, a traditional DisCSP with privacy requirements is viewed as a planning problem. The actions available to agents are: communication and local inference. Common decentralized solvers are evaluated here from the point of view of their interpretation as greedy planners. Further, we investigate some simple extensions where these solvers start taking into account the utility function. In these extensions we assume that the planning problem is further restricting the set of communication actions to only the communication primitives present in the corresponding solver protocols. The solvers obtained for the new type of problems propose the action (communication/inference) to be performed in each situation, defining thereby the policy.