Scalable parallel graph algorithms with matrix–vector multiplication evaluated with queries

Graph problems are significantly harder to solve with large graphs residing on disk compared to main memory only. In this work, we study how to solve four important graph problems: reachability from a source vertex, single source shortest path, weakly connected components, and PageRank. It is well k...

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Bibliographic Details
Published in:Distributed and parallel databases : an international journal Vol. 35; no. 3-4; pp. 335 - 362
Main Authors: Cabrera, Wellington, Ordonez, Carlos
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2017
Springer Nature B.V
Subjects:
Algorithms
Computer Science
Data base management systems
Data management
Data Structures
Database Management
Graph algorithms
Information Systems Applications (incl.Internet)
Iterative methods
Mathematical analysis
Matrix algebra
Matrix methods
Memory Structures
Multiplication
Operating Systems
Performance assessment
Queries
Query languages
Rings (mathematics)
Search engines
Shortest-path problems
Special Issue on In-Database Analytics
Data distribution
Parallel computation
Graph
Columnar DBMS
Array DBMS
ISSN:0926-8782, 1573-7578
Online Access:Get full text
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Summary:Graph problems are significantly harder to solve with large graphs residing on disk compared to main memory only. In this work, we study how to solve four important graph problems: reachability from a source vertex, single source shortest path, weakly connected components, and PageRank. It is well known that the aforementioned algorithms can be expressed as an iteration of matrix–vector multiplications under different semi-rings. Based on this mathematical foundation, we show how to express the computation with standard relational queries and then we study how to efficiently evaluate them in parallel in a shared-nothing architecture. We identify a common algorithmic pattern that unifies the four graph algorithms, considering a common mathematical foundation based on sparse matrix–vector multiplication. The net gain is that our SQL-based approach enables solving “big data” graph problems on parallel database systems, debunking common wisdom that they are cumbersome and slow. Using large social networks and hyper-link real data sets, we present performance comparisons between a columnar DBMS, an open-source array DBMS, and Spark’s GraphX.
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ISSN:0926-8782
1573-7578
DOI:10.1007/s10619-017-7200-6