Approximate parallel prefix computation and its applications

The authors address two fundamental problems in parallel algorithm design-parallel prefix sums and integer sorting-and show that both of them can be approximately solved very quickly on a randomized CRCW PRAM. In the case of prefix sums the approximation is in terms of the accuracy of the sums and in the case of integer sorting it is in terms of allowing some gaps between consecutive elements in the ordered list. By introducing approximation in these ways the authors are able to solve these problems in o(lg lg n) time, and thus avoid the near-logarithmic lower bounds by Beame and Hastad that hold for the exact versions of these problems. Nevertheless, they demonstrate that these approximations are strong enough to be used as subroutines in fast randomized algorithms for some well-known problems in parallel computational geometry. Perhaps the most succinct way to describe the power of the new tools which are presented is by observing that prior to this work it was known how to solve the interval allocation problem fast. The authors show how to solve the ordered version of the problem