Ismel Brito

Distributed forward checking

A reason to distribute constraint satisfaction is privacy: agents may not want to share their values, and they may wish to keep constraints as private as possible. In this paper, we present the Distributed Forward Checking algorithm, a natural successor of Asynchronous Backtracking, where some privacy is achieved on agent values. Regarding constraints, we introduce the Partially Known Constraints model, which allow a constraint between two agents to be not completely known by any of them. With these elements, we obtain new solving algorithms that enforce privacy and maintain completeness. Empirical results are provided. This research is supported by the REPLI project TIC-2002-04470-C03-03.

Distributed constraint satisfaction with partially known constraints

Distributed constraint satisfaction problems (DisCSPs) are composed of agents connected by constraints. The standard model for DisCSP search algorithms uses messages containing assignments of agents. It assumes that constraints are checked by one of the two agents involved in a binary constraint, hence the constraint is fully known to both agents. This paper presents a new DisCSP model in which constraints are kept private and are only partially known to agents. In addition, value assignments can also be kept private to agents and not be circulated in messages. Two versions of a new asynchronous backtracking algorithm that work with partially known constraints (PKC) are presented. One is a two-phase asynchronous backtracking algorithm and the other uses only a single phase. Another new algorithm preserves the privacy of assignments by performing distributed forward-checking (DisFC). We propose to use entropy as quantitative measure for privacy. An extensive experimental evaluation demonstrates a trade-off between preserving privacy and the efficiency of search, among the different algorithms.

Synchronous, asynchronous and hybrid algorithms for DisCSP

There is some debate around the efficiency of synchronous and asynchronous backtracking algorithms for solving DisCSP. The general opinion was that asynchronous algorithms were more efficient than the synchronous ones, because of their higher concurrency. In this work we continue this line of research, and we study the performance of three different procedures, one synchronous, one asynchronous and one hybrid, for solving sparse, medium and dense binary random DisCSP. The synchronous algorithm is SCBJ, a distributed version of the Conflict-Based Backjumping (CBJ) algorithm. The asynchronous algorithm is the standard ABT [2] enhanced with some heuristic. The hybrid algorithm is ABT-Hyb, a novel ABT-like algorithm, where some synchronization is introduced to avoid resending redundant messages. ABT-Hyb behaves like ABT when no backtracking is performed. However, when an agent has to backtrack, it sends a Back message and enters in a waiting state until receiving: a message that allows it to have a value consistent with its agent view, an Info message from the receiver of the last Back message or a Stop message informing that the problem has no solution. During the waiting state, the agent accept any received Info message and rejects as obsolete any received Back message. No matter the synchronous backtracking, ABT-Hyb inherits the good theoretical properties of ABT: it is sound, complete and terminates. This research is supported by the REPLI project TIC-2002-04470-C03-03.

Distributed stable matching problems

We consider the Stable Marriage Problem and the Stable Roommates Problem, two well-known types of the general class of Stable Matching Problems. They are combinatorial problems which can be solved by centralized algorithms in polynomial time. This requires to make public lists of preferences which agents would like to keep private. With this aim, we define the distributed version of these problems, and we provide a constraint-based approach that solves them keeping privacy. We give empirical results on the proposed approach. Supported by the Spanish REPLI project TIC-2002-04470-C03-03.

Connecting ABT with Arc Consistency

ABT is the reference algorithm for asynchronous distributed constraint satisfaction. When searching, ABT produces nogoods as justifications of deleted values. When one of such nogoods has an empty left-hand side, the considered value is eliminated unconditionally, once and for all. This value deletion can be propagated using standard arc consistency techniques, producing new deletions in the domains of other variables. This causes substantial reductions in the search effort required to solve a class of problems. We also extend this idea to the propagation of conditional deletions, something already proposed in the past. We provide experimental results that show the benefits of the proposed approach, especially considering communication cost.

Distributed forward checking may lie for privacy

DisFC is an ABT-like algorithm that, instead of sending the value taken by the high priority agent, it sends the domain of the low priority agent that is compatible with that value. With this strategy, plus the use of sequence numbers, some privacy level is achieved. In particular, each agent knows its value in the solution, but ignores the values of the others. However, the idea of sending the whole compatible domain each time an agent changes its value may cause a privacy loss on shared constraints that was initially overlooked. To solve this issue, we propose DisFClies, an algorithm that works like DisFC but it may lie about the compatible domains of other agents. It requires a single extra condition: if an agent sends a lie, it has to tell the truth in finite time afterwards. We prove that the algorithm is sound, complete and terminates. We provide experimental results on the increment in privacy achieved, at the extra cost of more search.

Improving ABT Performance by Adding Synchronization Points

Asynchronous Backtracking (ABT ) is a reference algorithm for Distributed CSP (DisCSP ). In ABT , agents assign values to their variables and exchange messages asynchronously and concurrently. When an ABT agent sends a backtracking message, it continues working without waiting for an answer. In this paper, we describe a case showing that this strategy may cause some inefficiency. To overcome this, we propose ABT hyb , a new algorithm that results from adding synchronization points to ABT . We prove that ABT hyb is correct, complete and terminates. We also provide an empirical evaluation of the new algorithm on several benchmarks. Experimental results show that ABT hyb outperforms ABT .