Elsevier

Discrete Applied Mathematics

Volume 39, Issue 3, 11 November 1992, Pages 231-240
Discrete Applied Mathematics

The capacity of the subarray partial concentrators

https://doi.org/10.1016/0166-218X(92)90178-DGet rights and content
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Abstract

A partial concentrator with parameters n, m, and c, is an n (inputs) × m (outputs) bipartile graph such that any set of k inputs, kc, has a perfect matching to some set of k outputs. A partial concentrator is regular if each input has M edges and each output has nMm edges. We study the problem of maximizing c for given m,n and M. For n=(mM)2 Kufta and Vacroux, and Richards and Hwang gave a similar construction of a partial concentrator and proved cM2+M−1. If, furthermore, mM is a prime, the construction given by Richards and Hwang has a cyclic property. In this paper we use this cyclic property to prove cM2+2M−2. This is the best result possible for M=3 since it coincides with an upper bound previously proved.

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