Communication-Aware Processor Allocation for Supercomputers

TL;DR

This paper develops algorithms for processor allocation in supercomputers that minimize communication hops, providing approximation guarantees and a PTAS, with experimental validation.

Contribution

It introduces a novel approximation algorithm and a PTAS for processor clustering problems in grid architectures, addressing complexity and practical performance.

Findings

7/4-approximation for 2D grids

Approximation guarantee of 2-(1/2d) in d dimensions

Experimental results validate the algorithms

Abstract

This paper gives processor-allocation algorithms for minimizing the average number of communication hops between the assigned processors for grid architectures, in the presence of occupied cells. The simpler problem of assigning processors on a free grid has been studied by Karp, McKellar, and Wong who show that the solutions have nontrivial structure; they left open the complexity of the problem. The associated clustering problem is as follows: Given n points in Re^d, find k points that minimize their average pairwise L1 distance. We present a natural approximation algorithm and show that it is a 7/4-approximation for 2D grids. For d-dimensional space, the approximation guarantee is 2-(1/2d), which is tight. We also give a polynomial-time approximation scheme (PTAS) for constant dimension d, and report on experimental results.