Slabpose Columnsort: A New Oblivious Algorithm for Out-of-Core Sorting on Distributed-Memory Clusters

Abstract

Our goal is to develop a robust out-of-core sorting program for a distributed-memory cluster. The literature contains two dominant paradigms for out-of-core sorting algorithms: merging-based and partitioningbased. We explore a third paradigm, that of oblivious algorithms. Unlike the two dominant paradigms, oblivious algorithms do not depend on the input keys and therefore lead to predetermined I/O and communication patterns in an out-of-core setting. Predetermined I/O and communication patterns facilitate overlapping I/O, communication, and computation for efficient implementation. We have developed several out-of-core sorting programs using the paradigm of oblivious algorithms. Our baseline implementation, 3-pass columnsort, was based on Leighton's columnsort algorithm. Though efficient in terms of I/O and communication, 3-pass columnsort has a restriction on the maximum problem size. As our first effort toward relaxing this restriction, we developed two implementations: subblock columnsort and M-columnsort. Both of these implementations incur substantial performance costs: subblock columnsort performs additional disk I/O, and M-columnsort needs substantial amounts of extra communication and computation. In this paper we present slabpose columnsort, a new oblivious algorithm that we have designed explicitly for the out-of-core setting. Slabpose columnsort relaxes the problem-size restriction at no extra I/O or communication cost. Experimental evidence on a Beowulf cluster shows that unlike subblock columnsort and M-columnsort, slabpose columnsort runs almost as fast as 3-pass columnsort. To the best of our knowledge, our implementations are the first out-of-core multiprocessor sorting algorithms that make no assumptions about the keys and produce output that is perfectly load balanced and in the striped order assumed by the Parallel Disk Model.

Oblivious vs. Distribution-Based Sorting: An Experimental Evaluation

“…In previous work, we have developed several implementations based on the paradigm of oblivious algorithms [CCW01,CC02,CCH,CC04].…”

Scalable distributed-memory external sorting

“…However, this value decreases when most nodes are used because the fabric gets overloaded (we have measured bandwidths as low as 400 MB/s). On every compute node, the 4 disks were configured as RAID-0 (striping) 7 . Each node contains 4 Seagate Barracuda 7200.10 hard drives with a capacity of 250 GB each.…”

“…This algorithm needs at least four passes over the data. 5 In [7] an algorithm based on column-sort is proposed that sorts up to (M/P ) 3/2 / √ 2 elements using three passes over the data. Using one additional pass, the input size can be increased to max(O M 3/2 , (M/P ) 5/3 ) elements.…”

Privacy-Preserving Access of Outsourced Data via Oblivious RAM Simulation

“…Unfortunately, many of the existing efficient external-memory sorting algorithms are not oblivious in this sense (e.g., see [2,42]). Alternatively, existing oblivious external-memory sorting algorithms [11] are not fully scalable to memories of size O(n ), or even smaller, which is what we need here. So we describe an efficient external-memory oblivious sorting algorithm, which is an external-memory k-way modular mergesort that is an external-memory adaptation of Lee and Batcher's generalization [32] of odd-even mergesort [8].…”