PC-DPOP: A Partial Centralization Extension of DPOP

A number of algorithms have been recently proposed for distributed constraint optimization problems (DCOP). Fully decentralized examples include ADOPT [11] (search) or DPOP [12] (dynamic programming). Difficult optimization problems have been shown to require important amounts of communication when these algorithms are used (large number of small messages for ADOPT, or few but large messages for DPOP). Alternatively, distributed-centralized hybrids that centralize parts of the problem have also been proposed. These algorithms have the potential of requiring small amounts of communication by centralizing parts of the problem, and solving them with a centralized algorithm. OptAPO [7] is such a hybrid. It operates as a cooperative mediation process, where agents designated as mediators centralize subproblems and solve them in dynamic and asynchronous mediation sessions. The authors show that its message complexity is significantly smaller than ADOPT’s. However, it is possible that several mediators solve overlapping problems, thus needlessly duplicating effort. Furthermore, the asynchronous and dynamic nature of the mediation sessions make it impossible to predict what will be centralized where, how much of the problem will be eventually centralized, or how big a computational burden will the mediators have to carry. This work introduces PC-DPOP, a new extension of DPOP. PCDPOP is also a hybrid that centralizes parts of the problem. However, it does so in a very directed and completely predictable way: difficult subproblems are clustered and centralized into the roots of the clusters. The subproblems that are centralized are always completely disjoint, thus avoiding all duplication of work. It allows for apriori, exact predictions of what will be centralized where, what amount of communication will be required over each link in the network, and what amount of effort will be needed in the centralizing nodes. Exact privacy loss assessments are also possible before the actual execution. Overall, the number of messages is linear as with DPOP. As opposed to DPOP, the message size is also kept under a user specified limit.