Parallel processing can be harmful: The unusual behavior of interpolation search

AbstractSeveral articles have noted the usefulness of a retrieval algorithm called sequential interpolation search, and Yao and Yao have proven a lower bound log logN−O(1), showing this algorithm is actually optimal up to an additive constant on unindexed files of sizeNgenerated by the uniform probability distribution. We generalize the latter to show log logN− log logP−O(1) lower bounds the complexity of any retrieval algorithm withPparallel processors for searching an unindexed file of sizeN. This result is surprising because we also show how to obtain an upper bound that matches the lower bound up to an additive constant with a procedure that actually usesno parallel processingoutside its last iteration (at which time our proposal turns onPprocessors in parallel). Our first theorem therefore states thatparallel processing before the literally last iterationin the search of an unindexed ordered file hasnearly no usefulness. Two further surprising facts are that the preceding result holds even when communication between the parallel processing units involvesno delayand that the parallel algorithms are actuallyinherently slowerthan their sequential counterparts when each invocation of the SIMD machine invokes a communication step withany typeof nonzerodelay. The presentation in the first two chapters of this paper is quite informal, so that the reader can quickly grasp the underlying intuition