DeepAI

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

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 general combinatorial objects. 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).

• 20 publications
• 7 publications
06/14/2019

### Combinatorial generation via permutation languages. I. Fundamentals

In this work we present a general and versatile algorithmic framework fo...
07/18/2021

### Efficient algorithms for maximum induced matching problem in permutation and trapezoid graphs

We first design an 𝒪(n^2) solution for finding a maximum induced matchin...
02/17/2020

### Hypergraph Isomorphism for Groups with Restricted Composition Factors

We consider the isomorphism problem for hypergraphs taking as input two ...
11/25/2021

### On the Difficulty of Evolving Permutation Codes

Combinatorial designs provide an interesting source of optimization prob...
02/02/2022

### Combinatorial Gray codes-an updated survey

A combinatorial Gray code for a class of objects is a listing that conta...
05/23/2018

### Rectangular Young tableaux with local decreases and the density method for uniform random generation (short version)

In this article, we consider a generalization of Young tableaux in which...
10/19/2019

### Semantic Limits of Dense Combinatorial Objects

The theory of limits of discrete combinatorial objects has been thriving...