STABCOL: an efficient implementation of the Weisfeiler-Leman algorithm
Abstract: "A coherent algebra is a matrix algebra over the field of the complex numbers which is closed under conjugate transposition and elementwise multiplication of matrices and which contains the identity matrix and the all 1 matrix. This algebraic structure has a variety of important appli...
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
München
1996
|
| Series: | Technische Universität <München>: TUM-MATH
9611 |
| Subjects: | |
| Summary: | Abstract: "A coherent algebra is a matrix algebra over the field of the complex numbers which is closed under conjugate transposition and elementwise multiplication of matrices and which contains the identity matrix and the all 1 matrix. This algebraic structure has a variety of important applications. Among others, coherent algebras are an appropriate tool in the design of algorithms for two notoriously hard graph theoretical problems: the problems of deciding whether two graphs are isomorphic and of finding the automorphism partition of a graph. Weisfeiler and Leman stated a polynomial algorithm which computes the coherent algebra which is generated by the adjacency matrix of a graph. However, for almost three decades, no reasonable time bound was known for this method. Very recently, one of the authors established a theoretical time bound of O(n³ log n) with n denoting the number of vertices in the graph. The aim of this paper is to document a computer implementation of the algorithm of Weisfeiler-Leman with the above-mentioned complexity. The program is called STABCOL and is coded in programming language C. We give a detailed description as well as a program listing and instructions how to use the program." |
| Physical Description: | 25 S. |
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| 520 | 3 | |a Abstract: "A coherent algebra is a matrix algebra over the field of the complex numbers which is closed under conjugate transposition and elementwise multiplication of matrices and which contains the identity matrix and the all 1 matrix. This algebraic structure has a variety of important applications. Among others, coherent algebras are an appropriate tool in the design of algorithms for two notoriously hard graph theoretical problems: the problems of deciding whether two graphs are isomorphic and of finding the automorphism partition of a graph. Weisfeiler and Leman stated a polynomial algorithm which computes the coherent algebra which is generated by the adjacency matrix of a graph. However, for almost three decades, no reasonable time bound was known for this method. Very recently, one of the authors established a theoretical time bound of O(n³ log n) with n denoting the number of vertices in the graph. The aim of this paper is to document a computer implementation of the algorithm of Weisfeiler-Leman with the above-mentioned complexity. The program is called STABCOL and is coded in programming language C. We give a detailed description as well as a program listing and instructions how to use the program." | |
| 650 | 4 | |a Algorithms | |
| 650 | 4 | |a Matrices | |
| 700 | 1 | |a Baumann, Stefan |e Verfasser |4 aut | |
| 700 | 1 | |a Lüdecke, Mariel |e Verfasser |4 aut | |
| 830 | 0 | |a Technische Universität <München>: TUM-MATH |v 9611 |w (DE-604)BV006186461 |9 9611 | |
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Record in the Search Index
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| author | Babel, Luitpold 1962- Baumann, Stefan Lüdecke, Mariel |
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| id | DE-604.BV011447448 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:09:56Z |
| institution | BVB |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007700013 |
| oclc_num | 38039475 |
| open_access_boolean | |
| owner | DE-12 DE-91G DE-BY-TUM |
| owner_facet | DE-12 DE-91G DE-BY-TUM |
| physical | 25 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| record_format | marc |
| series | Technische Universität <München>: TUM-MATH |
| series2 | Technische Universität <München>: TUM-MATH |
| spelling | Babel, Luitpold 1962- Verfasser (DE-588)1215213646 aut STABCOL an efficient implementation of the Weisfeiler-Leman algorithm Luitpold Babel ; Stefan Baumann ; Mariel Lüdecke München 1996 25 S. txt rdacontent n rdamedia nc rdacarrier Technische Universität <München>: TUM-MATH 9611 Abstract: "A coherent algebra is a matrix algebra over the field of the complex numbers which is closed under conjugate transposition and elementwise multiplication of matrices and which contains the identity matrix and the all 1 matrix. This algebraic structure has a variety of important applications. Among others, coherent algebras are an appropriate tool in the design of algorithms for two notoriously hard graph theoretical problems: the problems of deciding whether two graphs are isomorphic and of finding the automorphism partition of a graph. Weisfeiler and Leman stated a polynomial algorithm which computes the coherent algebra which is generated by the adjacency matrix of a graph. However, for almost three decades, no reasonable time bound was known for this method. Very recently, one of the authors established a theoretical time bound of O(n³ log n) with n denoting the number of vertices in the graph. The aim of this paper is to document a computer implementation of the algorithm of Weisfeiler-Leman with the above-mentioned complexity. The program is called STABCOL and is coded in programming language C. We give a detailed description as well as a program listing and instructions how to use the program." Algorithms Matrices Baumann, Stefan Verfasser aut Lüdecke, Mariel Verfasser aut Technische Universität <München>: TUM-MATH 9611 (DE-604)BV006186461 9611 |
| spellingShingle | Babel, Luitpold 1962- Baumann, Stefan Lüdecke, Mariel STABCOL an efficient implementation of the Weisfeiler-Leman algorithm Technische Universität <München>: TUM-MATH Algorithms Matrices |
| title | STABCOL an efficient implementation of the Weisfeiler-Leman algorithm |
| title_auth | STABCOL an efficient implementation of the Weisfeiler-Leman algorithm |
| title_exact_search | STABCOL an efficient implementation of the Weisfeiler-Leman algorithm |
| title_full | STABCOL an efficient implementation of the Weisfeiler-Leman algorithm Luitpold Babel ; Stefan Baumann ; Mariel Lüdecke |
| title_fullStr | STABCOL an efficient implementation of the Weisfeiler-Leman algorithm Luitpold Babel ; Stefan Baumann ; Mariel Lüdecke |
| title_full_unstemmed | STABCOL an efficient implementation of the Weisfeiler-Leman algorithm Luitpold Babel ; Stefan Baumann ; Mariel Lüdecke |
| title_short | STABCOL |
| title_sort | stabcol an efficient implementation of the weisfeiler leman algorithm |
| title_sub | an efficient implementation of the Weisfeiler-Leman algorithm |
| topic | Algorithms Matrices |
| topic_facet | Algorithms Matrices |
| volume_link | (DE-604)BV006186461 |
| work_keys_str_mv | AT babelluitpold stabcolanefficientimplementationoftheweisfeilerlemanalgorithm AT baumannstefan stabcolanefficientimplementationoftheweisfeilerlemanalgorithm AT ludeckemariel stabcolanefficientimplementationoftheweisfeilerlemanalgorithm |