Summary: Expanders, sorting in rounds
and superconcentrators of
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA 02139
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 n-superconcen-
trators of limited depth. For example, we construct an n supercon-
centrator of depth 3 with O(n4j3) edges; better than the previous