The bisection width and the isoperimetric number of arrays

Authors:
M. Cemil Azizoğlu;Ömer Eğecioğlu
Affiliations:
Akamai Technologies Inc., 6815 Flanders Dr., Suite 150, San Diego, CA;Department of Computer Science, University of California, Santa Barbara, CA
Venue:
Discrete Applied Mathematics - Optimal discrete structure and algorithms (ODSA 2000)
Year:
2004

Citing 5
Cited 1

Isoperimetric numbers of graphs

Journal of Combinatorial Theory Series B
Introduction to parallel algorithms and architectures: array, trees, hypercubes

Introduction to parallel algorithms and architectures: array, trees, hypercubes
Linear Layouts of Generalized Hypercubes

WG '93 Proceedings of the 19th International Workshop on Graph-Theoretic Concepts in Computer Science
The Edge-isoperimetric Number of Generalized Cylinders

The Edge-isoperimetric Number of Generalized Cylinders
Extremal Sets Minimizing Dimension-Normalized Boundary in Hamming Graphs

SIAM Journal on Discrete Mathematics

Bisection (band)width of product networks with application to data centers

TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

We prove that the bisection width, bw(Ad), of a d-dimensional array Ad = Pk1 × Pk2 × ... × Pkd where k1≤k2≤ ...≤kd, is given by bw(Ad) = Σdi=e Ki where e is the largest index for which ke is even (if it exists, e = 1 otherwise) and Ki = ki-1ki-2 ... k1. We also show that the edge-isoperimetric number i(Ad) is given by i(Ad) = 1/[kd/2]. Furthermore, a bisection and an isoperimetric set are constructed.