Fast Sorting on the Sequent

We develop a series of quicksort algorithms for the Sequent Symmetry shared memory parallel computer. By employing a novel yet simple parallel splitting algorithm and dynamic scheduling we are able to achieve a speedup of 13 with 16 processors over the performance of sequential quicksort on one processor. This work provides experimental evidence that asynchronous algorithms’ more uniform usage of shared resources may make them less susceptible to bottlenecks on real machines. Introduction: On sequential processors, Quicksort is one of the most e cient algorithms for sorting large arrays of data [Hoa62]. Three factors are eminently responsible for its speed: locality of memory references, a tight inner loop, and, on average, a small number of comparisons. Locality ensures both that cache prefetching can be exploited and that paging is minimal. Because a high proportion of the inner loop operations are comparisons, the computational overhead per comparison is small. Even though some other sequential sorting algorithms perform hardly any more, and possibly fewer, comparisons in the worst case than Quicksort performs on the average [Weg90], Quicksort remains the algorithm of choice over a wide range of input sizes due to its e ciency on real machines. Attempts to parallelize Quicksort are evident in the literature of both theory and practice. Some of the relevant theoretical work on parallel Quicksort is based on PRAM [FW78] models of computation in which the number of processors available is unlimited, and access to memory locations are of constant cost independent of address and of the number of processors active. Martel and Gusfield [MG89] and Chlebus and Vrťo [CV91], for example, describe formulations of Quicksort on the PRAM model sorting N distinct keys in O(logN) expected time with N processors. Other PRAM variants of Quicksort are described in Akl [Akl85] and JáJá [JáJ92]. There is nothing intrinsically wrong with such PRAM algorithms, but certain ⇤Max-Planck Institute for Computer Science, Saarbruecken, Germany. [email protected] †Department of Computer Science & Engineering, University of Washington, Seattle, WA. [email protected]