Abstract
Multiround algorithms are now commonly used in distributed data processing systems, yet the extent to which algorithms can benefit from running more rounds is not well understood. This paper answers this question for several rounds for the problem of computing the equijoin of n relations. Given any query Q with width w, intersection width iw, input size IN, output size OUT, and a cluster of machines with M=\Omega(IN \frac{1}{\epsilon}) memory available per machine, where \epsilon > 1 and w \ge 1 are constants, we show that:
1. Q can be computed in O(n) rounds with O(n(INw + OUT)2/M) communication cost with high probability.
Q can be computed in O(log(n)) rounds with O(n(INmax(w, 3iw) + OUT)2/M) communication cost with high probability.
Intersection width is a new notion we introduce for queries and generalized hypertree decompositions (GHDs) of queries that captures how connected the adjacent components of the GHDs are.
We achieve our first result by introducing a distributed and generalized version of Yannakakis's algorithm, called GYM. GYM takes as input any GHD of Q with width w and depth d, and computes Q in O(d + log(n)) rounds and O(n (INw + OUT)2/M) communication cost. We achieve our second result by showing how to construct GHDs of Q with width max(w, 3iw) and depth O(log(n)). We describe another technique to construct GHDs with longer widths and lower depths, demonstrating other tradeoffs one can make between communication and the number of rounds.
BibTeX  Entry
@InProceedings{afrati_et_al:LIPIcs:2017:7046,
author = {Foto N. Afrati and Manas R. Joglekar and Christopher M. Re and Semih Salihoglu and Jeffrey D. Ullman},
title = {{GYM: A Multiround Distributed Join Algorithm}},
booktitle = {20th International Conference on Database Theory (ICDT 2017)},
pages = {4:14:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770248},
ISSN = {18688969},
year = {2017},
volume = {68},
editor = {Michael Benedikt and Giorgio Orsi},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/7046},
URN = {urn:nbn:de:0030drops70462},
doi = {10.4230/LIPIcs.ICDT.2017.4},
annote = {Keywords: Joins, Yannakakis, Bulk Synchronous Processing, GHDs}
}
Keywords: 

Joins, Yannakakis, Bulk Synchronous Processing, GHDs 
Collection: 

20th International Conference on Database Theory (ICDT 2017) 
Issue Date: 

2017 
Date of publication: 

17.03.2017 