Linear Algebra Approach for Directed Triad Counting and Enumeration
Triangle counting and enumeration are commonly used in real-world applications on directed graphs. However, the performance of triangle counting algorithms is usually bench-marked on undirected graphs. As such, many of these algorithms and formulations are not suitable for identifying the types of d...
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| Vydáno v: | SC24-W: Workshops of the International Conference for High Performance Computing, Networking, Storage and Analysis s. 718 - 726 |
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17.11.2024
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| Abstract | Triangle counting and enumeration are commonly used in real-world applications on directed graphs. However, the performance of triangle counting algorithms is usually bench-marked on undirected graphs. As such, many of these algorithms and formulations are not suitable for identifying the types of directed triangles in directed graphs. In this work, we show how algorithms for counting each type of directed triad (directed triangle) can be formulated using linear algebra. Leveraging the FLAME methodology, we show that provably correct counting and enumeration algorithms for directed triads can be derived from the linear algebraic formulation. These algorithms can be used to count individual triads or together to count all possible triads. We show that despite being designed for individual use, the combined use of these algorithms yields a geometric mean speedup of 92.69x and 2.86x over the implementations in NetworkX and GraphBLAS (SuiteSparse 7.6), respectively, on various workloads from real-world directed graphs. |
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| AbstractList | Triangle counting and enumeration are commonly used in real-world applications on directed graphs. However, the performance of triangle counting algorithms is usually bench-marked on undirected graphs. As such, many of these algorithms and formulations are not suitable for identifying the types of directed triangles in directed graphs. In this work, we show how algorithms for counting each type of directed triad (directed triangle) can be formulated using linear algebra. Leveraging the FLAME methodology, we show that provably correct counting and enumeration algorithms for directed triads can be derived from the linear algebraic formulation. These algorithms can be used to count individual triads or together to count all possible triads. We show that despite being designed for individual use, the combined use of these algorithms yields a geometric mean speedup of 92.69x and 2.86x over the implementations in NetworkX and GraphBLAS (SuiteSparse 7.6), respectively, on various workloads from real-world directed graphs. |
| Author | Kerdcharoen, Yuttapichai Sangpetch, Orathai Low, Tze Meng Sridhar, Upasana |
| Author_xml | – sequence: 1 givenname: Yuttapichai surname: Kerdcharoen fullname: Kerdcharoen, Yuttapichai email: ykerdcha@andrew.cmu.edu organization: Carnegie Mellon University,Department of Electrical and Computer Engineering,Pittsburgh,PA,USA – sequence: 2 givenname: Upasana surname: Sridhar fullname: Sridhar, Upasana email: upasanas@cmu.edu organization: Carnegie Mellon University,Department of Electrical and Computer Engineering,Pittsburgh,PA,USA – sequence: 3 givenname: Orathai surname: Sangpetch fullname: Sangpetch, Orathai email: orathai@cmkl.ac.th organization: CMKL University,Department of Electrical and Computer Engineering,Bangkok,Thailand – sequence: 4 givenname: Tze Meng surname: Low fullname: Low, Tze Meng email: lowt@cmu.edu organization: Carnegie Mellon University,Department of Electrical and Computer Engineering,Pittsburgh,PA,USA |
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| Snippet | Triangle counting and enumeration are commonly used in real-world applications on directed graphs. However, the performance of triangle counting algorithms is... |
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| SubjectTerms | Conferences Directed graphs Fires graph algorithms High performance computing Linear algebra Object recognition Optimization Single instruction multiple data Systematics triad census |
| Title | Linear Algebra Approach for Directed Triad Counting and Enumeration |
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