Towards systematic parallel programming of graph problems via tree decomposition and tree parallelism

  • Authors:

  • Qi Wang;Meixian Chen;Yu Liu;Zhenjiang Hu

  • Affiliations:

  • Shanghai Jiao Tong University, Shanghai, China;Shanghai Jiao Tong University, Shanghai, China;The Graduate University for Advanced Studies, Tokyo, Japan;National Institute of Informatics, Tokyo, Japan

  • Venue:
  • Proceedings of the 2nd ACM SIGPLAN workshop on Functional high-performance computing
  • Year:
  • 2013

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Abstract

Many graph optimization problems, such as the Maximum Weighted Independent Set problem, are NP-hard. For large scale graphs that have billions of edges or vertices, these problems are hard to be computed directly even using popular data-intensive frameworks like MapReduce or Pregel that are deployed on large computer-clusters, because of the extremely high computational complexity. On the other hand, many studies have shown the existence of polynomial time algorithms on graphs with bounded treewidth, which makes it possible to solve these problems on large graphs. However, the algorithms are usually difficult to be understood or parallelized. In this paper, we propose a novel programming framework which provides a user-friendly programming interface and automatic in-black-box parallelization. The programming interface, which is a simple and straightforward abstraction called Generate-Test-Aggregate (GTA for short), is used to describe a set of graph problems. We propose to derive bottom-up dynamic programming algorithms on tree decompositions from the user-specified GTA algorithms, and further transform the bottom-up algorithms to parallel ones which run in a divide-and-conquer manner on a list of subtrees. Besides, balanced tree partition strategies are discussed for efficient parallel computing. Our preliminary experimental results on the Maximum Weighted Independent Set problem demonstrate the practical viability of our approaches.