 
Summary: Expanders, sorting in rounds
and superconcentrators of
limited depth
Noga Alon'
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA 02139
A b&act
Expanding graphs and superconccntrators are relevant to theoreti
cal computer science in several ways. Here WCuse finite geometries
to construct explicitly highly expanding graphs with essentially the
smallest possible number of edges.
Our graphs enable us to improve significantly previous results
on a parallel sorting problem, by descrilbing an explicit algorithm
to sort n elements in k time units using O(nPk) processors, where,
e.g., ap = 7/4.
Using our graphs we can also construct efficient nsuperconcen
trators of limited depth. For example, we construct an n supercon
centrator of depth 3 with O(n4j3) edges; better than the previous
known results.
