Truly efficient parallel algorithms: c-optimal multisearch for an extension of the BSP model

Abstract

In this paper we design and analyse parallel algorithms with the goal to get exact bounds on their speed-ups on real machines. For this purpose we define an extension of Valiant's BSP model, BSP^*, that rewards blockwise communication, and uses Valiant's notion of c-optimality. Intuitively a c-optimal parallel algorithm for p processors achieves speed-up close to p/c. We consider the Multisearch problem: Assume a strip in 2D to be partitioned into m segments. Given n query points in the strip, the task is to locate, for each query, its segment. For m ≤ n we present a deterministic BSP^* algorithm that is 1-optimal, if n = Ω(p log² p). For m > n, we present a randomized BSP^* algorithm that is (1 + δ)-optimal for arbitrary δ>0, m ≤ 2^p and n=Ω(p log² p). Both results hold for a wide range of BSP^* parameters where the range becomes larger with growing input sizes m and n. We further report on implementation work in progress. Previous parallel algorithms for Multisearch were far away from being c-optimal in our model and do not consider blockwise communication.

Supported in part by DFG-Sonderforschungsbereich 1511 “Massive Parallelität: Algorithmen, Entwurfsmethoden, Anwendungen”, by DFG Leibniz Grant Me872/6-1, and by the Esprit Basic Research Action Nr 7141 (ALCOM II)