In the efficient social choice problem, the goal is to assign values, subject to side constraints, to a set of variables to maximize the total utility across a population of agents, where each agent has private information about its utility function. In this paper we model the social choice problem as a distributed constraint optimization problem (DCOP), in which each agent can communicate with other agents that share an interest in one or more variables. Whereas existing DCOP algorithms can be easily manipulated by an agent, either by misreporting private information or deviating from the algorithm, we introduce M-DPOP, the first DCOP algorithm that provides a faithful distributed implementation for efficient social choice. This provides a concrete example of how the methods of mechanism design can be unified with those of distributed optimization. Faithfulness ensures that no agent can benefit by unilaterally deviating from any aspect of the protocol, neither informationrevelation, computation, nor communication, and whatever the private information of other agents. We allow for payments by agents to a central bank, which is the only central authority that we require. To achieve faithfulness, we carefully integrate the Vickrey-Clarke-Groves (VCG) mechanism with the DPOP algorithm, such that each agent is only asked to perform computation, report

Abstract. We propose ODPOP, a new distributed algorithm for open multiagent combinatorial optimization [3]. The ODOP algorithm explores the same search space as the dynamic programming algorithm DPOP [10] or the AND/OR search algorithm AOBB [2], but does so in an incremental, best-first fashion suitable for open problems. ODPOP has several advantages over DPOP. First, it uses messages whose size only grows linearly with the treewidth of the problem. Second, by letting agents explore values in a non-increasing order of preference, it saves a significant amount of messages and computation over the basic DPOP algorithm. To show the merits of our approach, we report on experiments with practically sized distributed meeting scheduling problems in a multiagent system. 1

A distributed constraint optimization problem (DCOP) is a formalism that captures the rewards and costs of local interactions within a team of agents. Because complete algorithms to solve DCOPs are unsuitable for some dynamic or anytime domains, researchers have explored incomplete DCOP algorithms that result in locally optimal solutions. One type of categorization of such algorithms, and the solutions they produce, is k-optimality; a k-optimal solution is one that cannot be improved by any deviation by k or fewer agents. This paper presents the first known guarantees on solution quality for k-optimal solutions. The guarantees are independent of the costs and rewards in the DCOP, and once computed can be used for any DCOP of a given constraint graph structure. 1

Abstract.Distributed Constraint Optimization (DCOP) is rapidly emerging as a prominent technique for multiagent coordination. Unfortunately, rigorous quantitative evaluations of privacy loss in DCOP algorithms have been lacking despite the fact that agent privacy is a key motivation for applying DCOPs in many applications. Recently, Maheswaran et al. [1, 2] introduced a framework for quantitative evaluations of privacy in DCOP algorithms, showing that early DCOP algorithms lose more privacy than purely centralized approaches and questioning the motivation for applying DCOPs. Do state-of-the art DCOP algorithms suffer from a similar shortcoming? This paper answers that question by investigating several of the most efficient DCOP algorithms, including both DPOP and ADOPT. Furthermore, while previous work investigated the impact on efficiency of distributed contraint reasoning design decisions, e.g. constraint-graph topology, asynchrony, message-contents, this paper examines the privacy aspect of such decisions, providing an improved understanding of privacy-efficiency tradeoffs. Finally, this paper augments previous work on system-wide privacy loss, by investigating inequities in individual agents ’ privacy loss. 1

Distributed Constraint Optimization (DCOP) is rapidly emerging as a prominent technique for multiagent coordination. However, despite agent privacy being a key motivation for applying DCOPs in many applications, rigorous quantitative evaluations of privacy loss in DCOP algorithms have been lacking. Recently, [Maheswaran et al.2005] introduced a framework for quantitative evaluations of privacy in DCOP algorithms, showing that some DCOP algorithms lose more privacy than purely centralized approaches and questioning the motivation for applying DCOPs. This paper addresses the question of whether state-of-the art DCOP algorithms suffer from a similar shortcoming by investigating several of the most efficient DCOP algorithms, including both DPOP and ADOPT. Furthermore, while previous work investigated the impact on efficiency of distributed contraint reasoning design decisions (e.g. constraint-graph topology, asynchrony, message-contents), this paper examines the privacy aspect of such decisions, providing an improved understanding of privacy-efficiency tradeoffs.

Fully decentralized algorithms for distributed constraint optimization often require excessive amounts of communication when applied to complex problems. The OptAPO algorithm of [Mailler and Lesser, 2004] uses a strategy of partial centralization to mitigate this problem. We introduce PC-DPOP, a new partial centralization technique, based on the DPOP algorithm of [Petcu and Faltings, 2005]. PC-DPOP provides better control over what parts of the problem are centralized and allows this centralization to be optimal with respect to the chosen communication structure. Unlike OptAPO, PC-DPOP allows for a priory, exact predictions about privacy loss, communication, memory and computational requirements on all nodes and links in the network. Upper bounds on communication and memory requirements can be specified. We also report strong efficiency gains over OptAPO in experiments on three problem domains. 1

Complete algorithms have been proposed to solve problems modelled as distributed constraint optimization (DCOP). However, there are only few attempts to address real world scenarios using this formalism, mainly because of the complexity associated with those algorithms. In the present work we compare three complete algorithms for DCOP, aiming at studying how they perform in complex and dynamic scenarios of increasing sizes. In order to assess their performance we measure not only standard quantities such as number of cycles to arrive to a solution, size and quantity of exchanged messages, but also computing time and quality of the solution which is related to the particular domain we use. This study can shed light in the issues of how the algorithms perform when applied to problems other than those reported in the literature (graph coloring, meeting scheduling, and distributed sensor network).

In distributed combinatorial optimization problems, dynamic programming algorithms like DPOP ([Petcu and Faltings, 2005]) require only a linear number of messages, thus generating low communication overheads. However, DPOP’s memory requirements are exponential in the induced width of the constraint graph, which may be prohibitive for problems with large width. We present MB-DPOP, a new hybrid algorithm that can operate with bounded memory. In areas of low width, MB-DPOP operates like standard DPOP (linear number of messages). Areas of high width are explored with bounded propagations using the idea of cycle-cuts [Dechter, 2003]. We introduce novel DFS-based mechanisms for determining the cycle-cutset, and for grouping cycle-cut nodes into clusters. We use caching ([Darwiche, 2001]) between clusters to reduce the complexity to exponential in the largest number of cycle cuts in a single cluster. We compare MB-DPOP with ADOPT [Modi et al., 2005], the current state of the art in distributed search with bounded memory. MB-DPOP consistently outperforms ADOPT on 3 problem domains, with respect to 3 metrics, providing speedups of up to 5 orders of magnitude. 1

Abstract. We present a framework for distributed combinatorial optimization. The framework is implemented in Java, and simulates a multiagent environment in a single Java virtual machine. Each agent in the environment is executed asynchronously in a separate execution thread, and communicates with its peers through message exchange. The framework is highly customizable, allowing the user to implement and experiment with any distributed optimization algorithm. Support for synchronous/asynchronous message passing, monitoring and statistics, as well as problem visualization tools are provided. A number of distributed algorithms are already implemented in this framework, like the Distributed Breakout Algorithm [17] and the DPOP Algorithm [13]. A number of random evaluation problems are also provided, from two distinct domains: meeting scheduling and resource allocation in a sensor network. 1

Distributed constraint optimization (DCOP) is a promising approach to coordination, scheduling and task allocation in multi agent networks. In large-scale or low-bandwidth networks, finding the global optimum is often impractical. K-optimality is a promising new approach: for the first time it provides us a set of locally optimal algorithms with quality guarantees as a fraction of global optimum. Unfortunately, previous work in k-optimality did not address domains where we may have prior knowledge of reward structure; and it failed to provide quality guarantees or algorithms for domains with hard constraints (such as agents ’ local resource constraints). This paper addresses these shortcomings with three key contributions. It provides: (i) improved lower-bounds on k-optima quality incorporating available prior knowledge of reward structure; (ii) lower bounds on k-optima quality for problems with hard constraints; and (iii) k-optimal algorithms for solving DCOPs with hard constraints and detailed experimental results on large-scale networks.