Faster symmetry discovery using sparsity of symmetries

• Published in: 2008 45th ACM/IEEE Design Automation Conference pp. 149 - 154
• Main Authors: Darga, Paul T., Sakallah, Karem A., Markov, Igor L.
• Format: Conference Proceeding
• Language: English
• Published: New York, NY, USA ACM 08-06-2008; IEEE
• Series: ACM Conferences
• Subjects: Boolean functions; Boolean satisfiability; constraint satisfaction problems; Electronic design automation and methodology; graph automorphism; Mathematics; Mathematics of computing > Discrete mathematics > Graph theory; Microprocessors; model checking; partition refinement; Partitioning algorithms; Permission; Personal digital assistants; Runtime; Space technology; sparsity; State-space methods; Symmetry; partition refinement; constraint satisfaction problems; model checking; symmetry; graph automorphism; sparsity; Boolean satisfiability
• ISBN: 1605581151; 9781605581156
• ISSN: 0738-100X
• DOI: 10.1145/1391469.1391509

Many computational tools have recently begun to benefit from the use of the symmetry inherent in the tasks they solve, and use general-purpose graph symmetry tools to uncover this symmetry. However, existing tools suffer quadratic runtime in the number of symmetries explicitly returned and are of limited use on very large, sparse, symmetric graphs. This paper introduces a new symmetry-discovery algorithm which exploits the sparsity present not only in the input but also the output, i.e., the symmetries themselves. By avoiding quadratic runtime on large graphs, it improves state-of-the-art runtimes from several days to less than a second.