Intel High Performance Data Analytics

Innovative convergence solutions in high performance data analytics and simulation software development using Intel architecture.
Vectorized Tree-like Subgraph Counting

Subgraph counting aims to count occurrences of a template T in a given network G(V, E). It is a powerful graph analysis tool and has found real-world applications in diverse domains.


Scaling subgraph counting problems is known to be memory bounded and computationally challenging with exponential complexity.


Challenges of Subgraph Counting:

  • Extremely high computational complexity. counting the exact number of subgraphs of size k in a n-vertex network takes O(n^k)time. Approximate  algorithm has a time complexity linear in network size, it is exponential to subgraph size.

  • Memory Access Efficiency. Graph Analytics algorithms usually have irregular and intensive random memory access, which is harmful to efficient cache prefetching.

  • SIMD Efficiency. Recent many-core architectures such as Intel Xeon Phi have “Vector processing units” (VPU), which only support SIMD programming mode, while graph analytics algorithms are difficult to be vectorized.

Our Approach:

  • Algorithmic Design: We convert the sequential color-coding algorithm to matrix operations.

  • System design and optimization. We design a data structure as well as a thread execution model to leverage the hardware efficiency of using linear-algebra kernels in terms of vector processing units (VPU) and memory bandwidth.

  • Portability to the distributed system and GPU. We scale out our single node implementation on a distributed system with near-linear strong scalability. In addition, we export the codes to NVIDIA GPU and NEC Vector Engine

We propose a novel vectorized subgraph counting algorithm, named Subgraph2Vec, as well as both shared memory and distributed implementations:

  1. Reducing algorithmic complexity by minimizing neighbor traversal;

  2. Achieving a highly-vectorized implementation upon linear algebra kernels to significantly improve performance and hardware utilization.

  3. Subgraph2Vec improves the overall performance over the state-of-the-art work by orders of magnitude and up to 660x on a single node.

  4. Subgraph2Vec in distributed mode can scale up the template size to 20 and maintain good strong scalability.

  5. Enabling portability to both CPU and GPU.


L.  Chen,  J.  Li,  C.  Sahinalp,  M.  Marathe,  A.  Vullikanti,  A.  Nikolaev, E.  Smirnov,  R.  Israfilov,  and  J.  Qiu,  “Subgraph2vec:   Highly-vectorized tree-like  subgraph  counting,”  in 2019 IEEE International Conference on Big Data, IEEE, 2019.


L. Chen, J.  Li , A. Azad, L. Jiang, A.  Vullikanti,  A.  Nikolaev, E.  Smirnov,  R.  Israfilov,  and  J.  Qiu,  "A GraphBLAS Approach for Subgraph Counting," arXiv preprint arXiv:1903.04395.


© 2021 Judy Fox

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