Geometric symmetry in graphs
Excluding Symmetries in Constraint-Based Search
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
Efficient Symmetry Breaking for Boolean Satisfiability
IEEE Transactions on Computers
Abstraction-based action ordering in planning
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Load balancing and almost symmetries for RAMBO quorum hosting
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
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Symmetry is a widespread phenomenon that can offer opportunities for powerful exploitation in areas as diverse as molecular chemistry, pure mathematics, circuit design, biology and architecture. Graphs are an abstract way to represent relational structures. The search for symmetry in many contexts can thus be reduced to the attempt to find graph automorphisms. Brendan McKay's NAUTY system (McKay 1990) is an example of one of the highly successful products of research into this task. Erdös and Rényi showed that almost all large graphs are asymmetric, but it is readily observed that many graphs representing structures of real Interest contain symmetry. Even more graphs are nearly symmmetric, in the sense that to each graph there is a closely Similar graph that is symmetric. In this paper we explore the problem of finding near symmetries in graphs and describe the techniques we are developing for performing this task.