Two-Attribute Skew Free, Isolated CP Theorem, and Massively Parallel Joins

This paper presents an algorithm to process a multi-way join with load $\tO(n/p^2/(α φ) )$ under the MPC model, where n is the number of tuples in the input relations, α the maximum arity of those relations, p the number of machines, and φ a newly introduced parameter called the \em generalized vertex packing number. The algorithm owes to two new findings. The first is a \em two-attribute skew free technique to partition the join result for parallel computation. The second is an \em isolated cartesian product theorem, which provides fresh graph-theoretic insights on joins with α \ge 3$ and generalizes an existing theorem on α = 2$.