Expanders, sorting in rounds and superconcentrators of limited depth

N Alon
1985 Proceedings of the seventeenth annual ACM symposium on Theory of computing - STOC '85  
A b&act Expanding graphs and superconccntrators are relevant to theoretical computer science in several ways. Here WC use 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
more » ... ficient n-superconcentrators of limited depth. For example, we construct an n superconcentrator of depth 3 with O(n4j3) edges; better than the previous known results.
doi:10.1145/22145.22156 dblp:conf/stoc/Alon85 fatcat:pksf5i2bt5debldvwk2kfk57gm