Marius Silaghi

Asynchronous aggregation and consistency in distributed constraint satisfaction

Constraint Satisfaction Problems (CSP) have been very successful in problem-solving tasks ranging from resource allocation and scheduling to configuration and design. Increasingly, many of these tasks pose themselves in a distributed setting where variables and constraints are distributed among different agents. A variety of asynchronous search algorithms have been proposed for addressing this setting. We show how two techniques commonly used in centralized constraint satisfaction, value aggregation and maintaining arc consistency can be applied to increase efficiency in an asynchronous, distributed context as well, and report on experiments that quantify the gains.

Meeting Scheduling Guaranteeing n/2-Privacy and Resistant to Statistical Analysis (Applicable to any DisCSP)

Distributed problems raise privacy issues. The user would like to specify securely his constraints (desires, availability, money) on his computer once. The computer is expected to compute and communicate for searching an acceptable solution while maintaining the privacy of the user. Even without computers infested with spy viruses that capture the interaction with the user, most agent based approaches reveal parts of one agents secret data to its partners in distributed computations [Using privacy loss to guide decisions in distributed CSP search]. Some cryptographic multi-party computation protocols [Completeness theorems for non-cryptographic fault-tolerant distributed computating] succeed to avoid leaking secrets at the computation of some functions with private inputs. They have been applied to find the set of all solutions for the meeting scheduling problem [On securely scheduling a meeting]. However, nobody yet succeeded to apply those techniques for finding a random solution to the meeting scheduling problem. Note that revealing all solutions, when you only need a single one, leaks a lot of data about when others are, or are not, available. Some answers were proposed in our previous approaches to distributed constraint problems [Solving a distributed CSP with cryptographic multi-party computations, without revealing constraints and without involving trusted servers]. They guarantee that no agent can infer with certitude a secret from the identity of the solution of the problem (other than the acceptance of the solution), but guarantee nothing about inference of probabilistic information about secrets. Our new technique answers this problem, too.

Distributed Search Method with Bounded Cost Vectors on Multiple Objective DCOPs

We generalize a pseudo-tree based solver to employ boundaries of multi-objective DCOPs. Multi-objective problems have been addressed in the research area of DCOPs recently. For the case of multiple objectives, the objective values are defined as the result of separate evaluation schemes. Applying multi-objectives to pseudo-tree based search is also important to generalize several traditional solvers. Here, we introduce boundaries for the vector of objective values in a solver based on pseudo-trees. Both the bottom-up computation of the partial dynamic-programming and the top-down computation of the tree-search employ the bounded vectors of the objective values. Several operations including aggregation, decomposition and comparison of objective values are extended for the bounded vectors.

Distributed Private Constraint Optimization

We merge two popular optimization criteria of distributed constraint optimization problems (DCOPs) -- reward-based utility and privacy -- into a single criterion. Privacy requirements on constraints has classically motivated an optimization criterion of minimizing the number of disclosed tuples, or maximizing the entropy about constraints. Common complete DCOP search techniques seek solutions minimizing the cost and maintaining some privacy. We start from the observation that for some problems we could provide as input a quantification of loss of privacy in terms of cost. We provide a formal way to integrate this new input parameter into the DCOP framework, discuss its implications and advantages.

Framework for Modeling Reordering Heuristics for Asynchronous Backtracking

Dynamic reordering of variables is known to be important for solving constraint satisfaction problems (CSPs). Efforts to apply this principle for improving polynomial space asynchronous backtracking (ABT) started with [A. Armstrong and E.F. Durfee, 1997], using a solution based on synchronization points. [M.-C. Silaghi et al., 2001] shows how to asynchronously enable reordering heuristics in ABT and proposes a general protocol called Asynchronous Backtracking with Reordering (ABTR). In this work we introduce a first framework for modeling heuristics possible with asynchronous backtracking. We also show that ABTR enables heuristics that displace even the agent requesting the reordering, as in the reordering of Dynamic Backtracking. They have not been illustrated in [M.-C. Silaghi et al., 2001]. The most efficient self-reordering heuristic that we introduce and experiment, approx-AWCl, is inspired from Asynchronous Weak-Commitment [M. Yokoo et al., 1998 ] and brings small but significant improvements, comparable to the results in [A. Armstrong and E.F. Durfee, 1997]. We also report that min-domain dynamic ordering heuristics for ABTR are worse than no reordering and better than max-domain (in experiments that also use maintenance of arc consistency).

Leximin Multiple Objective Optimization for Preferences of Agents

We address a variation of Multiple Objective Distributed Constraint Optimization Problems (MODCOPs). In the conventional MODCOPs, a few objectives are globally defined and agents cooperate to find the Pareto optimal solution. On the other hand, in several practical problems, the share of each agent is important. Such shares are represented as preference values of agents. This class of problems is defined as the MODCOP on the preferences of agents. Particularly, we focus on the optimization problems based on the leximin ordering (Leximin AMODCOPs), which improves the equality among agents. The solution methods based on pseudo trees are applied to the Leximin AMODCOPs.

Reducing the search space of resource constrained DCOPs

Distributed constraint optimization problems (DCOPs) have been studied as a basic framework of multi-agent cooperation. The Resource Constrained DCOP (RCDCOP) is a special DCOP framework that contains n-ary hard constraints for shared resources. In RCDCOPs, for a value of a variable, a certain amount of the resource is consumed. Upper limits on the total use of resources are defined by n-ary resource constraints. To solve RCDCOPs, exact algorithms based on pseudotrees employ virtual variables whose values represent use of the resources. Although, virtual variables allow for solving the problems without increasing the depth of the pseudo-tree, they exponentially increase the size of search spaces. Here, we reduce the search space of RCDCOPs solved by a dynamic programming method. Several boundaries of resource use are exploitable to reduce the size of the tables. To employ the boundaries, additional pre-processing and further filtering are applied. As a result, infeasible solutions are removed from the tables. Moreover, multiple elements of the tables are aggregated into fewer elements. By these modifications, redundancy of the search space is removed. One of our techniques reduces the size of the messages by an order of magnitude.

Constant Cost of the Computation-Unit in Efficiency Graphs for DCOP Solvers

We show how to ensure a constant cost for the computation-unit in graphs depicting the number of (sequential) computation-units at different (distributed) problem sizes. We report empirical evaluation with ADOPT revealing that the computation cost associated with constraint check (commonly used - and assumed constant - in ENCCCs evaluations) actually varies with the problem size, by orders of magnitude. We therefore propose better computation-units based on a basket of weighted constraint-checks and contexts processing operations.

Leximin Asymmetric Multiple Objective Distributed Constraint Optimization Problem

The Distributed Constraint Optimization Problem (DCOP) lies at the foundations of multiagent cooperation. With DCOPs, the optimization in distributed resource allocation problems is formalized using constraint optimization problems. The solvers for the problem are designed based on decentralized cooperative algorithms that are performed by multiple agents. In a conventional DCOP, a single objective is considered.

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.