Concurrency in heavily loaded neighborhood-constrained systems

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Abstract

Let G be a connected undirected graph in which each node corresponds to a process and two nodes are connected by an edge if the corresponding processes share a resource. We consider distributed computations in which processes are constantly demanding all of their resources in order to operate, and in which neighboring processes may not operate concurrently. We advocate that such a system is general enough for representing a large class of resource-sharing systems under heavy load. We employ a distributed scheduling mechanism based on acyclic orientations of G and investigate the amount of concurrency that it provides. We show that this concurrency is given by a number akin to G 's chromatic and multichromatic numbers, and that, among scheduling schemes which require neighbors in G to alternate in their turns to operate, ours is the one that potentially provides the greatest concurrency. However, we also show that the decision problem corresponding to optimizing concurrency is NP -complete.