Reconfigurable cellular computers

Abstract

When a collection of processors P 1 ,,P n< operates in parallel, it is desirable that at any given stage of the computation, each {ifP i should have a task of about the same size to perform, and each {ifP i should require about the same amount of information from the other P 's in order to perform its task. To the extent that these conditions are violated, parallelism is impaired, in the sense that the P 's are not all used with equal efficiency. In cellular computers, e.g., as they might be used for parallel image processing, these conditions are maintained by having the P 's all perform similar computations on different parts of the input data, and by allowing each P i to receive information from a fixed set of the others (its “neighbors≓), where these sets are all of bounded size. This paper discusses, on an abstract level, the concept of a reconfigurable cellular computer, in which each P i can receive information from a set S i of the other P 's, and the S i 's areall of bounded size, but they need not remain fixed throughout a computation. Requiring the S i 's to have bounded size implies that most P 's cannot communicate directly; the expected time required for two arbitrary P 's to communicate depends on the graph structure defined by the sets S i . The question of how to change the S i 's in parallel during the course of a computation is also discussed.