# A unifying method for the design of algorithms canonizing combinatorial objects

arXiv: https://arxiv.org/abs/1806.07466 · HTML: https://mlsanity.com/paper/1806.07466/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2018.

## Built on by (most cited first, 1 of 1)

- [Instruction Set and Language for Hypergraphs](https://mlsanity.com/paper/2607.10194/) (2026)

## Abstract (arXiv)

We devise a unified framework for the design of canonization algorithms. Using hereditarily finite sets, we define a general notion of combinatorial objects that includes graphs, hypergraphs, relational structures, codes, permutation groups, tree decompositions, and so on. Our approach allows for a systematic transfer of the techniques that have been developed for isomorphism testing to canonization. We use it to design a canonization algorithm for combinatorial objects in general. This result gives new fastest canonization algorithms with an asymptotic running time matching the best known isomorphism algorithm for the following types of objects: hypergraphs, hypergraphs of bounded color class size, permutation groups (up to permutational isomorphism) and codes that are explicitly given (up to code equivalence).