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Smaller Explicit Superconcentrators (Extended Abstract)
 

Summary: Smaller Explicit Superconcentrators
(Extended Abstract)
N. Alon
M. Capalbo
July 28, 2002
Abstract
Using a new recursive technique, we present an explicit construction of an infinite
family of N-superconcentrators of density 44. The most economical previously known
explicit graphs of this type have density around 60.
1 Introduction
For an integer N, an N-superconcentrator N is a directed acyclic graph with a set X of N
inputs (i.e., vertices with indegree 0) and a set Y of N outputs (i.e., vertices with outdegree
0), such that, for any subset S of X, and any subset T of Y satisfying |S| = |T|, there are
|S| vertex-disjoint directed paths in N from S to T. Superconcentrators have many applica-
tions in Computer Science, and the explicit construction of sparse graphs of this type has been
a problem studied extensively. Gaber and Galil [4] presented the first explicit construction
of N-superconcentrators with O(N) edges (more precisely, about 270N edges). Since then,
several researchers [2], [3], [5], [9], and [1] presented constructions of N-superconcentrators
using fewer and fewer directed edges. The most economical construction before the one de-
scribed in the present paper has been obtained from the technique presented in [1], combined

  

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

 

Collections: Mathematics