 
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 Nsuperconcentrators of density 44. The most economical previously known
explicit graphs of this type have density around 60.
1 Introduction
For an integer N, an Nsuperconcentrator 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 vertexdisjoint 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 Nsuperconcentrators with O(N) edges (more precisely, about 270N edges). Since then,
several researchers [2], [3], [5], [9], and [1] presented constructions of Nsuperconcentrators
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
