Julien Vion

Second-order consistencies

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.

Multi-variable distributed backtracking with sessions

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.

Path consistency by dual consistency

Dual Consistency (DC) is a property of Constraint Networks (CNs) which is equivalent, in its unrestricted form, to Path Consistency (PC). The principle is to perform successive singleton checks (i.e. enforcing arc consistency after the assignment of a value to a variable) in order to identify inconsistent pairs of values, until a fixpoint is reached. In this paper, we propose two new algorithms, denoted by sDC2 and sDC3, to enforce (strong) PC following the DC approach. These algorithms can be seen as refinements of Mac Gregors algorithm as they partially and totally exploit the incrementality of the underlying Arc Consistency algorithm. While sDC3 admits the same interesting worst-case complexities as PC8, sDC2 appears to be the most robust algorithm in practice. Indeed, compared to PC8 and the optimal PC2001, sDC2 is usually around one order of magnitude faster on large instances.

From MDD to BDD and Arc consistency

In this paper, we present a new conversion of multivalued decision diagrams (MDD) to binary decision diagrams (BDD) which can be used to improve MDD-based fil- tering algorithms such as MDDC or MDD-4R. We also propose BDDF, an algorithm that copies modified parts of the BDD “on the fly” during the search of a solution, and yields a better incrementality than a pure MDDC-like approach. MDDC is not very efficient when used to represent poorly structured positive table constraints. Our new representation combined with BDDF retains the properties of the MDD representation and has comparable performances to the STR2 algorithm by Ullmann (2007) and Lecoutre (Constraints, 16.4, 341–371 2011).

Replication in Fault-Tolerant Distributed CSP

Real life problems can be solved by a distributed way, in particular by multi-agent approaches. However, the fault tolerance is not guarantee when an agent, for example, does not have any activity (e.g. it dies). This problem is very crucial, when the interactional model is based on a Distributed CSP. Many algorithms have been proposed in the literature, but they give wrong results if an agent dies. This paper presents an approach which is based on a replication principle: each local CSP is replicated in another agent.

DisCSPs with Privacy Recast as Planning Problems for Self-Interested Agents

Much of the Distributed Constraint Satisfaction Problem (DisCSP) solving research has addressed cooperating agents, and privacy was frequently mentioned as a significant motivation of the decentralization. While privacy may have a role for cooperating agents, it is easier understood in the context of self-interested utility-based agents, and this is the situation considered here. With utility-based agents, the DisCSP framework can be extended to model privacy and satisfaction under the concept of utility. We introduce Utilitarian Distributed Constraint Satisfaction Problems (UDisCSP), an extension of the DisCSP that exploits the rewards for finding a solution and the costs for losing privacy as guidance for the utility-based agents. A parallel can be drawn between Partially Observable Markov Decision Processes (POMDPs) and the problems solved by individual agents for UDisCSPs. Common DisCSP solvers are extended to take 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 ones available in the corresponding solver protocols. The solvers obtained propose the action to be performed in each situation, defining thereby the policy of the agents.

Integrating strong local consistencies into constraint solvers

This article presents a generic scheme for adding strong local consistencies to the set of features of constraint solvers, which is notably applicable to event-based constraint solvers. We encapsulate a subset of constraints into a global constraint. This approach allows a solver to use different levels of consistency for different subsets of constraints in the same model. Moreover, we show how strong consistencies can be applied with different kinds of constraints, including user-defined constraints. We experiment our technique with a coarse-grained algorithm for Max-RPC, called Max-RPCrm, and a variant of it, L-Max-RPCrm. Experiments confirm the interest of strong consistencies for Constraint Programming tools.

Fault Tolerance in DisCSPs: Several Failures Case

To solve a distributed problem in presence of a failed entity, we have to find a way to accomplish the failed entity tasks. In this paper, we present an approach which guarantees the resolution of DisCSPs in presence of failed agents. This approach is based on local CSPs replication principle: each failed agent local CSP is replicated in another agent which will support it. Obtained results confirm that our approach can solve a DisCSP in presence of failed agents by giving a solution when it exists.