The exploitation of data locality in parallel computers is paramount to reduce the memory traac and communication among processing nodes. We focus on the exploitation of locality by Parallel Radix sort. The original Parallel Radix sort has several communication steps in which one sorting key may have to visit several processing nodes. In response to this, we propose a reorganization of Radix so...

Sample sort, a generalization of quicksort that partitions the input into many pieces, is known as the best practical comparison based sorting algorithm for distributed memory parallel computers. We show that sample sort is also useful on a single processor. The main algorithmic insight is that element comparisons can be decoupled from expensive conditional branching using predicated instructio...

Sorting on interconnection networks has been solved ‘optimally’. However, the ‘lowerorder’ terms are so large that they dominate the overall time-consumption for many practical problem sizes. Particularly for deterministic algorithms, this is a serious problem. In this paper a refined deterministic sampling strategy is presented, by which the additional term of the presented deterministic sorti...

This means we cannot justify the correctness of the “Partition” subroutine by the Hoare’s axiom on program verification. This article is organized as follows. First, we present several fundamental properties of “while” program and finite sequence. Second, we define the “Partition” subroutine on SCMPDS, the task of which is to split a sequence into a smaller and a larger subsequence. The definit...

Barsalou’s elision of the personal and sub-personal levels tends to conceal the fact that he is, at best, providing the “specs” but not yet a model for his hypothesized perceptual symbols. John Maynard Keynes was once asked if he thought in words or pictures. “I think in thoughts,” the great man is reported to have replied. Fair enough, but now what? What kind of things are thoughts, and how do...

This means we cannot justify the correctness of the “Partition” subroutine by the Hoare’s axiom on program verification. This article is organized as follows. First, we present several fundamental properties of “while” program and finite sequence. Second, we define the “Partition” subroutine on SCMPDS, the task of which is to split a sequence into a smaller and a larger subsequence. The definit...

The goal of the PennySort benchmark is to reflect the progress done by technology, in particular, evolvement of I/O OS subsystems and file systems. This benchmark measures what data volume can be sorted for “one penny” on a system, which cost is distributed over three years. This work decribes how to build a cost-effective system for this competition, using our high-performance external algorit...

Sorting is an important component of many applications, and parallel sorting algorithms have been studied extensively in the last three decades. One of the earliest parallel sorting algorithms is Bitonic Sort, which is represented by a sorting network consisting of multiple butterfly stages. This paper studies bitonic sort on modern parallel machines which are relatively coarse grained and cons...

We recount the history of a new qsort function for a C library. Our function is clearer, faster and more robust than existing sorts. It chooses partitioning elements by a new sampling scheme; it partitions by a novel solution to Dijkstra’s Dutch National Flag problem; and it swaps efficiently. Its behavior was assessed with timing and debugging testbeds, and with a program to certify performanc...

This paper investigates how to improve the worst case runtime of INSERTION SORT while keeping it in-place, incremental and adaptive. To sort an array of n elements with w bits for each element, classic INSERTION SORT runs in O(n) operations with wn bits space. GAPPED INSERTION SORT has a runtime of O(n lg n) with a high probability of only using (1+ )wn bits space. This paper shows that ROTATED...