A generic framework for engineering graph canonization algorithms

The state-of-the-art tools for practical graph canonization are all based on the individualization-refinement paradigm, and their di erence is primarily in the choice of heuristics they include and in the actual tool implementation. It is thus not possible to make a direct comparison of how individual algorithmic ideas a ect the performance on di erent graph classes. We present an algorithmic software framework that facilitates implementation of heuristics as independent extensions to a common core algorithm. It therefore becomes easy to perform a detailed comparison of the performance and behaviour of di erent algorithmic ideas. Implementations are provided of a range of algorithms for tree traversal, target cell selection, and node invariant, including choices from the literature and new variations. The framework readily supports extraction and visualization of detailed data from separate algorithm executions for subsequent analysis and development of new heuristics. Using collections of di erent graph classes we investigate the e ect of varying the selections of heuristics, often revealing exactly which individual algorithmic choice is responsible for particularly good or bad performance. On several benchmark collections, including a newly proposed class of di cult instances, we additionally find that our implementation performs better than the current state-of-the-art tools.