An Agglomeration Law for Sorting Networks and its Application in Functional Programming

TL;DR

This paper introduces a general agglomeration law for sorting networks that enhances parallelization and adaptability in functional programming, enabling efficient hybrid sorting algorithms on modern hardware.

Contribution

It presents a novel agglomeration law for sorting networks that maintains structure while generalizing input handling, improving parallelization and integration with functional programming.

Findings

Effective parallelization on multicore and GPGPU architectures

Enables hybrid sorting algorithms using sorting networks as merging stages

Demonstrated efficiency through Eden language implementation

Abstract

In this paper we will present a general agglomeration law for sorting networks. Agglomeration is a common technique when designing parallel programmes to control the granularity of the computation thereby finding a better fit between the algorithm and the machine on which the algorithm runs. Usually this is done by grouping smaller tasks and computing them en bloc within one parallel process. In the case of sorting networks this could be done by computing bigger parts of the network with one process. The agglomeration law in this paper pursues a different strategy: The input data is grouped and the algorithm is generalized to work on the agglomerated input while the original structure of the algorithm remains. This will result in a new access opportunity to sorting networks well-suited for efficient parallelization on modern multicore computers, computer networks or GPGPU programming. Additionally this enables us to use sorting networks as (parallel or distributed) merging stages for arbitrary sorting algorithms, thereby creating new hybrid sorting algorithms with ease. The expressiveness of functional programming languages helps us to apply this law to systematically constructed sorting networks, leading to efficient and easily adaptable sorting algorithms. An application example is given, using the Eden programming language to show the effectiveness of the law. The implementation is compared with different parallel sorting algorithms by runtime behaviour.