  In this paper we propose and prove that cyclic quorum sets can efficiently
manage all-pairs computations and data replication. The quorums are
O(N/sqrt(P)) in size, up to 50% smaller than the dual N/sqrt(P) array
implementations, and significantly smaller than solutions requiring all data.
Implementation evaluation demonstrated scalability on real datasets with a 7x
speed up on 8 nodes with 1/3rd the memory usage per process. The all-pairs
problem requires all data elements to be paired with all other data elements.
These all-pair problems occur in many science fields, which has led to their
continued interest. Additionally, as datasets grow in size, new methods like
these that can reduce memory footprints and distribute work equally across
compute nodes will be demanded.
