Duality Between Prefetching and Queued Writing with Parallel Disks

This is the published version, made available with the permission of the publisher. Copyright © 2005 Society for Industrial and Applied Mathematics.Parallel disks promise to be a cost effective means for achieving high bandwidth in applications involving massive data sets, but algorithms for parallel disks can be difficult to devise. To combat this problem, we define a useful and natural duality between writing to parallel disks and the seemingly more difficult problem of prefetching. We first explore this duality for applications involving read-once accesses using parallel disks. We get a simple linear time algorithm for computing optimal prefetch schedules and analyze the efficiency of the resulting schedules for randomly placed data and for arbitrary interleaved accesses to striped sequences. Duality also provides an optimal schedule for prefetching plus caching, where blocks can be accessed multiple times. Another application of this duality gives us the first parallel disk sorting algorithms that are provably optimal up to lower-order terms. One of these algorithms is a simple and practical variant of multiway mergesort, addressing a question that had been open for some time

Duality Between Prefetching and Queued Writing with Parallel Disks

AMS subject classifications. 68W10, 68W20, 68W40, 68M20, 68P10, 68P20, 68Q17 DOI. 10.1137/S0097539703431573Parallel disks promise to be a cost effective means for achieving high bandwidth in applications involving massive data sets, but algorithms for parallel disks can be difficult to devise. To combat this problem, we define a useful and natural duality between writing to parallel disks and the seemingly more difficult problem of prefetching. We first explore this duality for applications involving read-once accesses using parallel disks. We get a simple linear time algorithm for computing optimal prefetch schedules and analyze the efficiency of the resulting schedules for randomly placed data and for arbitrary interleaved accesses to striped sequences. Duality also provides an optimal schedule for prefetching plus caching, where blocks can be accessed multiple times. Another application of this duality gives us the first parallel disk sorting algorithms that are provably optimal up to lower-order terms. One of these algorithms is a simple and practical variant of multiway mergesort, addressing a question that had been open for some time

Algorithmic ramifications of prefetching in memory hierarchy

External Memory models, most notable being the I-O Model [3], capture the effects of memory hierarchy and aid in algorithm design. More than a decade of architectural advancements have led to new features not captured in the I-O model - most notably the prefetching capability. We propose a relatively simple Prefetch model that incorporates data prefetching in the traditional I-O models and show how to design algorithms that can attain close to peak memory bandwidth. Unlike (the inverse of) memory latency, the memory bandwidth is much closer to the processing speed, thereby, intelligent use of prefetching can considerably mitigate the I-O bottleneck. For some fundamental problems, our algorithms attain running times approaching that of the idealized Random Access Machines under reasonable assumptions. Our work also explains the significantly superior performance of the I-O efficient algorithms in systems that support prefetching compared to ones that do not

Algorithm Libraries for Multi-Core Processors

By providing parallelized versions of established algorithm libraries, we ease the exploitation of the multiple cores on modern processors for the programmer. The Multi-Core STL provides basic algorithms for internal memory, while the parallelized STXXL enables multi-core acceleration for algorithms on large data sets stored on disk. Some parallelized geometric algorithms are introduced into CGAL. Further, we design and implement sorting algorithms for huge data in distributed external memory

An Efficient Multiway Mergesort for GPU Architectures

Sorting is a primitive operation that is a building block for countless algorithms. As such, it is important to design sorting algorithms that approach peak performance on a range of hardware architectures. Graphics Processing Units (GPUs) are particularly attractive architectures as they provides massive parallelism and computing power. However, the intricacies of their compute and memory hierarchies make designing GPU-efficient algorithms challenging. In this work we present GPU Multiway Mergesort (MMS), a new GPU-efficient multiway mergesort algorithm. MMS employs a new partitioning technique that exposes the parallelism needed by modern GPU architectures. To the best of our knowledge, MMS is the first sorting algorithm for the GPU that is asymptotically optimal in terms of global memory accesses and that is completely free of shared memory bank conflicts. We realize an initial implementation of MMS, evaluate its performance on three modern GPU architectures, and compare it to competitive implementations available in state-of-the-art GPU libraries. Despite these implementations being highly optimized, MMS compares favorably, achieving performance improvements for most random inputs. Furthermore, unlike MMS, state-of-the-art algorithms are susceptible to bank conflicts. We find that for certain inputs that cause these algorithms to incur large numbers of bank conflicts, MMS can achieve up to a 37.6% speedup over its fastest competitor. Overall, even though its current implementation is not fully optimized, due to its efficient use of the memory hierarchy, MMS outperforms the fastest comparison-based sorting implementations available to date

Parallel Out-of-Core Sorting: The Third Way

Sorting very large datasets is a key subroutine in almost any application that is built on top of a large database. Two ways to sort out-of-core data dominate the literature: merging-based algorithms and partitioning-based algorithms. Within these two paradigms, all the programs that sort out-of-core data on a cluster rely on assumptions about the input distribution. We propose a third way of out-of-core sorting: oblivious algorithms. In all, we have developed six programs that sort out-of-core data on a cluster. The first three programs, based completely on Leighton\u27s columnsort algorithm, have a restriction on the maximum problem size that they can sort. The other three programs relax this restriction; two are based on our original algorithmic extensions to columnsort. We present experimental results to show that our algorithms perform well. To the best of our knowledge, the programs presented in this thesis are the first to sort out-of-core data on a cluster without making any simplifying assumptions about the distribution of the data to be sorted