**Reference**:- Michael A. Bender, David P. Bunde, Erik D. Demaine, Sándor P. Fekete, Vitus J. Leung, Henk Meijer, and Cynthia A. Phillips, “Communication-Aware Processor Allocation for Supercomputers”, in
*Proceedings of the 9th Workshop on Algorithms and Data Structures (WADS 2005)*, Lecture Notes in Computer Science, volume 3608, Waterloo, Ontario, Canada, August 15–17, 2005, pages 169–181. **Abstract**:-
We give processor-allocation algorithms for grid architectures,
where the objective is to select processors from a set of available
processors to minimize the average number of communication hops.
The associated clustering problem is as follows: Given
*n*points in**R**^{d}, find a size-*k*subset with minimum average pairwise*L*_{1}distance. We present a natural approximation algorithm and show that it is a 7/4-approximation for 2D grids. In*d*dimensions, the approximation guarantee is 2 − 1/(2*d*), which is tight. We also give a polynomial-time approximation scheme (PTAS) for constant dimension*d*and report on experimental results. **Comments**:- This paper is also available as arXiv:cs.DS/0407058 of the Computing Research Repository (CoRR), and from SpringerLink.
**Copyright**:- The paper is \copyright Springer-Verlag.
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Last updated January 13, 2020 by Erik Demaine.