Alexandros V Gerbessiotis and Constantinos J Siniolakis
May 1996, 28pp.
The implementation of data structures on distributed memory models such as the Bulk-Synchronous Parallel (BSP) model, rather than shared memory ones such as the PRAM, offers a serious challenge. In this work we undertake the architecture independent study of the communication and synchronization requirements of searching ordered h-level graphs, which include most of the standard data structures. We propose multi-way search as a general tool for the design, analysis, and implementation of BSP algorithms. This technique allows elegant high-level design and analysis of algorithms, using data structures similar to those of sequential models. Applications to computational geometry and sorting are also presented. In particular, our new randomized sorting algorithm improves previously known BSP randomized sorting algorithms upon both the high-probability bounds and the amount of parallel slackness required to achieve optimality. Moreover, our methods are within a 1 + o(1) multiplicative factor of the respective sequential methods.
While our methods are fairly simple themselves, description of their performance in terms of the BSP parameters is somewhat complicated. The main reward for quantifying these complications, is that it enables software to be written once and for all that can be migrated efficiently among a variety of parallel machines.