A note on weighted distributed match-making

In many distributed computing environments, processes are concurrently executed by nodes in a store-and-forward network. Distributed control issues as diverse as name-server, mutual exclusion, and replicated data management, involve making matches between processes. The generic paradigm is a formal problem called “distributed match-making.” We define multidimensional and weighted versions, and the relations between the two, and develop a very general method to prove lower bounds on the complexity as a tradeoff between number of messages and “distributedness.” The resulting lower bounds are tight in all cases we have examined. We present a success-stop version of distributed match-making that is analysed in terms of a weight distribution that in all cases results in approximately halving the (expected) number of messages required in the corresponding strategy that does not use these weights. The second author did part of this work at the Laboratory for Computer Science, M.I.T., Cambridge, MA. He was supported in part by the Office of Naval Research under Contract N00014-85-K-0168, by the Office of Army Research under Contract DAAG29-84-K-0058, by the National Science Foundation under Grant DCR-83-02391, and by the Defence Advanced Research Projects Agency (DARPA) under Contract N00014-83-K-0125. A preliminary version of this paper appeared inProc. VLSI Algorithms and Architectures, 3rd Aegean Workshop on Computing (AWOC 88), Lecture Notes in Computer Science, vol. 319, Springer-Verlag, Berlin, 1988, pp. 361–368.