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A Characterization of Individualization-Refinement Trees
Markus Anders, Jendrik Brachter, Pascal Schweitzer
Individualization-Refinement (IR) algorithms form the standard method and currently the only practical method for symmetry computations of graphs and combinatorial objects in gener…
Parallel Computation of Combinatorial Symmetries
Markus Anders, Pascal Schweitzer
In practice symmetries of combinatorial structures are computed by transforming the structure into an annotated graph whose automorphisms correspond exactly to the desired symmetri…
Comparative Design-Choice Analysis of Color Refinement Algorithms Beyond the Worst Case
Markus Anders, Pascal Schweitzer, Florian Wetzels
Color refinement is a crucial subroutine in symmetry detection in theory as well as practice. It has further applications in machine learning and in computational problems from lin…
Engineering a Fast Probabilistic Isomorphism Test
Markus Anders, Pascal Schweitzer
We engineer a new probabilistic Monte-Carlo algorithm for isomorphism testing. Most notably, as opposed to all other solvers, it implicitly exploits the presence of symmetries with…
Search Problems in Trees with Symmetries: near optimal traversal strategies for individualization-refinement algorithms
Markus Anders, Pascal Schweitzer
We define a search problem on trees that closely captures the backtracking behavior of all current practical graph isomorphism algorithms. Given two trees with colored leaves, the…