Sorting-Based Selection Algorithms for Hypercubic Networks

Abstract.

This paper presents several deterministic algorithms for selecting the k th largest record from a set of n records on any n -node hypercubic network. All of the algorithms are based on the selection algorithm of Cole and Yap, as well as on various sorting algorithms for hypercubic networks. Our fastest algorithm runs in O( lg n lg ^* n) time, very nearly matching the trivial $\Omega(\lg n)$ lower bound. Previously, the best upper bound known for selection was O( lg n lg lg n) . A key subroutine in our O( lg n lg^* n) time selection algorithm is a sparse version of the Sharesort algorithm that sorts n records using p processors, $p\geq n$ , in O( lg n ( lg lg p - lg lg (p/n) ) ² ) time.