Parallel Acyclic Joins with Canonical Edge Covers
Yufei Tao
TL;DR
This paper introduces a new mathematical structure called 'canonical edge cover' for acyclic hypergraphs, providing a novel analysis of an existing MPC algorithm for acyclic joins, and explaining its optimality through graph-theoretic properties.
Contribution
It presents a new analysis of Hu's MPC algorithm using the concept of canonical edge covers, offering deeper theoretical understanding of its effectiveness.
Findings
Revealed the 'canonical edge cover' structure for acyclic hypergraphs.
Proved properties of canonical edge covers that explain algorithm performance.
Provided a graph-theoretic perspective on acyclic join processing.
Abstract
In PODS'21, Hu presented an algorithm in the massively parallel computation (MPC) model that processes any acyclic join with an asymptotically optimal load. In this paper, we present an alternative analysis of her algorithm. The novelty of our analysis is in the revelation of a new mathematical structure -- which we name "canonical edge cover" -- for acyclic hypergraphs. We prove non-trivial properties for canonical edge covers that offer us a graph-theoretic perspective about why Hu's algorithm works.
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