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Counting and uniform sampling of directed acyclic graphs (DAGs) from a Markov equivalence class are fundamental tasks in graphical causal analysis. In this paper, we show that these tasks can be performed in polynomial time, solving a…

Machine Learning · Computer Science 2020-12-18 Marcel Wienöbst , Max Bannach , Maciej Liśkiewicz

We introduce the framework of Deep Weisfeiler Leman algorithms (DeepWL), which allows the design of purely combinatorial graph isomorphism tests that are more powerful than the well-known Weisfeiler-Leman algorithm. We prove that, as an…

Logic in Computer Science · Computer Science 2020-03-25 Martin Grohe , Pascal Schweitzer , Daniel Wiebking

Notions of graph similarity provide alternative perspective on the graph isomorphism problem and vice-versa. In this paper, we consider measures of similarity arising from mismatch norms as studied in Gervens and Grohe: the edit distance…

Discrete Mathematics · Computer Science 2026-05-07 He Sun , Danny Vagnozzi

We extend Babai's quasipolynomial-time graph isomorphism test (STOC 2016) and develop a quasipolynomial-time algorithm for the multiple-coset isomorphism problem. The algorithm for the multiple-coset isomorphism problem allows to exploit…

Data Structures and Algorithms · Computer Science 2020-04-21 Daniel Wiebking

We propose a simple and efficient local algorithm for graph isomorphism which succeeds for a large class of sparse graphs. This algorithm produces a low-depth canonical labeling, which is a labeling of the vertices of the graph that…

Probability · Mathematics 2023-09-20 Julia Gaudio , Miklós Z. Rácz , Anirudh Sridhar

We give an overview of recent advances on the graph isomorphism problem. Our main focus will be on Babai's quasi-polynomial time isomorphism test and subsequent developments that led to the design of isomorphism algorithms with a…

Data Structures and Algorithms · Computer Science 2021-01-15 Martin Grohe , Daniel Neuen

Given a graph $G$, the graph $[G]$ obtained by adding, for each pair of vertices of $G$, a unique vertex adjacent to both vertices is called the binding graph of $G$. In this work, we show that the class of binding graphs is…

Combinatorics · Mathematics 2024-08-27 Rui Xue

Combining the the results of A.R. Meyer and L.J. Stockmeyer "The Equivalence Problem for Regular Expressions with Squaring Requires Exponential Space", and K.S. Booth "Isomorphism testing for graphs, semigroups, and finite automata are…

Computational Complexity · Computer Science 2007-08-31 Matthew Delacorte

Color refinement is a classical technique used to show that two given graphs G and H are non-isomorphic; it is very efficient, although it does not succeed on all graphs. We call a graph G amenable to color refinement if it succeeds in…

Computational Complexity · Computer Science 2015-05-05 V. Arvind , Johannes Köbler , Gaurav Rattan , Oleg Verbitsky

Graphs with high symmetry or regularity are the main source for experimentally hard instances of the notoriously difficult graph isomorphism problem. In this paper, we study the computational complexity of isomorphism testing for line…

Computational Complexity · Computer Science 2018-07-03 Michael Huber

Graph isomorphism, a classical algorithmic problem, determines whether two input graphs are structurally identical or not. Interestingly, it is one of the few problems that is not yet known to belong to either the P or NP-complete…

Data Structures and Algorithms · Computer Science 2024-10-01 Sourav Dutta , Arnab Bhattacharya

The graph isomorphism problem is a main problem which has numerous applications in different fields. Thus, finding an efficient and easy to implement method to discriminate non-isomorphic graphs is valuable. In this paper, a new method is…

Combinatorics · Mathematics 2016-11-08 Ameneh Farhadian

The complexity of the graph isomorphism problem for trapezoid graphs has been open over a decade. This paper shows that the problem is GI-complete. More precisely, we show that the graph isomorphism problem is GI-complete for comparability…

Discrete Mathematics · Computer Science 2016-01-20 Asahi Takaoka

The Graph Isomorphism (GI) problem is a theoretically interesting problem because it has not been proven to be in P nor to be NP-complete. Babai made a breakthrough in 2015 when announcing a quasipolynomial time algorithm for GI problem.…

Data Structures and Algorithms · Computer Science 2020-02-13 Duc Hung Pham , Krishna V. Palem , M. V. Panduranga Rao

Soient donn\'es deux graphes $\Gamma_1$, $\Gamma_2$ \`a $n$ sommets. Sont-ils isomorphes? S'ils le sont, l'ensemble des isomorphismes de $\Gamma_1$ \`a $\Gamma_2$ peut \^etre identifi\'e avec une classe $H \pi$ du groupe sym\'etrique sur…

Group Theory · Mathematics 2017-10-13 Harald Andrés Helfgott

The min-rank of a graph was introduced by Haemers (1978) to bound the Shannon capacity of a graph. This parameter of a graph has recently gained much more attention from the research community after the work of Bar-Yossef et al. (2006). In…

Combinatorics · Mathematics 2016-11-26 Son Hoang Dau , Yeow Meng Chee

As it follows from G\"odel's incompleteness theorems, any consistent formal system of axioms and rules of inference should imply a true unprovable statement. Actually, this fundamental principle can be efficiently applicable in…

Data Structures and Algorithms · Computer Science 2020-11-25 Roman Galay , Daniil Kalistratov

We show that the number of $k$-matching in a given undirected graph $G$ is equal to the number of perfect matching of the corresponding graph $G_k$ on an even number of vertices divided by a suitable factor. If $G$ is bipartite then one can…

Computational Complexity · Computer Science 2016-08-31 Shmuel Friedland , Daniel Levy

A right [left] locally testable language S is a language with the property that for some non negative integer k two words u and v in alphabet S are equal in the semi group if (1) the prefix and suffix of the words of length k coincide, (2)…

Formal Languages and Automata Theory · Computer Science 2020-11-10 A. N. Trahtman

The graph isomorphism problem is considered. We assign modified $n$-variable characteristic polynomials for graphs and reduce the graph isomorphism problem to the problem of the polynomials isomorphism. It is required to find out, is there…

Discrete Mathematics · Computer Science 2024-10-18 Alexander Prolubnikov