Related papers: Canonical Labelling of Site Graphs
Symmetries of combinatorial objects are known to complicate search algorithms, but such obstacles can often be removed by detecting symmetries early and discarding symmetric subproblems. Canonical labeling of combinatorial objects…
We show that if $p=O(1/n)$, then the Erd\H{o}s-R\'{e}nyi random graph $G(n,p)$ with high probability admits a canonical labeling computable in time $O(n\log n)$. Combined with the previous results on the canonization of random graphs, this…
Graph alignment in two correlated random graphs refers to the task of identifying the correspondence between vertex sets of the graphs. Recent results have characterized the exact information-theoretic threshold for graph alignment in…
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…
We state a combinatorial optimization problem whose feasible solutions define both a decomposition and a node labeling of a given graph. This problem offers a common mathematical abstraction of seemingly unrelated computer vision tasks,…
Binary classification problems can be naturally modeled as bipartite graphs, where we attempt to classify right nodes based on their left adjacencies. We consider the case of labeled bipartite graphs in which some labels and edges are not…
Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called…
An assignment of colours to the vertices of a graph is stable if any two vertices of the same colour have identically coloured neighbourhoods. The goal of colour refinement is to find a stable colouring that uses a minimum number of…
We prove that there exists an algorithm for determining whether two piecewise-linear spatial graphs are isomorphic. In its most general form, our theorem applies to spatial graphs furnished with vertex colorings, edge colorings and/or edge…
The individualization-refinement paradigm for computing a canonical labeling and the automorphism group of a graph is investigated. A new algorithmic design aimed at reducing the size of the associated search space is introduced, and a new…
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…
We prove that whenever $d=d(n)\to\infty$ and $n-d\to\infty$ as $n\to\infty$, then with high probability for any non-trivial initial colouring, the colour refinement algorithm distinguishes all vertices of the random regular graph…
We show that a canonical labeling of a random $n$-vertex graph can be obtained by assigning to each vertex $x$ the triple $(w_1(x),w_2(x),w_3(x))$, where $w_k(x)$ is the number of walks of length $k$ starting from $x$. This takes time…
Graph labelling is one of the noticed contexts in combinatorics and graph theory. Graceful labelling for a graph $G$ with $e$ edges, is to label the vertices of $G$ with $0, 1, \cdots, e$ such that, if we specify to each edge the difference…
In this paper, we show a connection between a certain online low-congestion routing problem and an online prediction of graph labeling. More specifically, we prove that if there exists a routing scheme that guarantees a congestion of…
In this study, we address the complex issue of graph clustering in signed graphs, which are characterized by positive and negative weighted edges representing attraction and repulsion among nodes, respectively. The primary objective is to…
Graph partition is a key component to achieve workload balance and reduce job completion time in parallel graph processing systems. Among the various partition strategies, edge partition has demonstrated more promising performance in…
Canonical orderings and their relatives such as st-numberings have been used as a key tool in algorithmic graph theory for the last decades. Recently, a unifying concept behind all these orders has been shown: they can be described by a…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
This paper develops two heuristic algorithms to solve graph isomorphism, using free energy encoding. The first algorithm uses four types of encoding refinement techniques such that every graph can be distinguished by a canonical number…