Related papers: The polynomial algorithm for graphs' isomorphism t…
We study the problems of testing isomorphism of polynomials, algebras, and multilinear forms. Our first main results are average-case algorithms for these problems. For example, we develop an algorithm that takes two cubic forms $f, g\in…
We give a fully polynomial randomized approximation scheme to compute a lower bound for the matching polynomial of any weighted graph at a positive argument. For the matching polynomial of complete bipartite graphs with bounded weights…
Vladimir Shpilrain and Jie-Tai Yu have asked for an effective algorithm to decide if two elements of C[x,y] are related by an automorphism of C[x,y]. We describe here an efficient algorithm that decides this question and finds the…
We present in this short note a polynomial graph extension procedure that can be used to improve any graph isomorphism algorithm. This construction propagates new constraints from the isomorphism constraints of the input graphs (denoted by…
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…
In this paper, we propose algorithms for the graph isomorphism (GI) problem that are based on the eigendecompositions of the adjacency matrices. The eigenvalues of isomorphic graphs are identical. However, two graphs $ G_A $ and $ G_B $ can…
We consider heuristic algorithm for solving graph isomorphism problem. The algorithm based on a successive splitting of the eigenvalues of the matrices which are modifications (to positive defined) of graphs' adjacency matrices.…
Graph isomorphism is an important computer science problem. The problem for the general case is unknown to be in polynomial time. The base algorithm for the general case works in quasi-polynomial time. The solutions in polynomial time for…
It's important to design polynomial time algorithms to test if two graphs are isomorphic at least for some special classes of graphs. An approach to this was presented by Eugene M. Luks(1981) in the work \textit{Isomorphism of Graphs of…
In a recent breakthrough, Babai (STOC 2016) gave a quasipolynomial time graph isomorphism test. In this work, we give an improved isomorphism test for graphs of small degree: our algorithms runs in time $n^{O((\log d)^{c})}$, where $n$ is…
A partial complement of the graph $G$ is a graph obtained from $G$ by complementing all the edges in one of its induced subgraphs. We study the following algorithmic question: for a given graph $G$ and graph class $\mathcal{G}$, is there a…
The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several…
In this paper we present an algorithm, called conauto-2.0, that can efficiently compute a set of generators of the automorphism group of a graph, and test whether two graphs are isomorphic, finding an isomorphism if they are. This algorithm…
Parameter testing algorithms are using constant number of queries to estimate the value of a certain parameter of a very large finite graph. It is well-known that graph parameters such as the independence ratio or the edit-distance from…
The graph isomorphism (GI) problem is the computational problem of finding a permutation of vertices of a given graph $G_1$ that transforms $G_1$ to another given graph $G_2$ and preserves the adjacency. In this work, we propose a quantum…
A polynomial complexity algorithm is designed which tests whether a point belongs to a given tropical linear variety.
The monography examines the problem of constructing a group of automorphisms of a graph. A graph automorphism is a mapping of a set of vertices onto itself that preserves adjacency. The set of such automorphisms forms a vertex group of a…
A hole in a graph G is an induced cycle of length at least four; an antihole is a hole in the complement of G. In 2005, Chudnovsky, Cornuejols, Liu, Seymour and Vuskovic showed that it is possible to test in polynomial time whether a graph…
We prove that there is a graph isomorphism test running in time $n^{\operatorname{polylog}(h)}$ on $n$-vertex graphs excluding some $h$-vertex graph as a minor. Previously known bounds were $n^{\operatorname{poly}(h)}$ (Ponomarenko, 1988)…
In this paper, we give algorithms for determining the existence of isomorphism between two finite-dimensional Lie algebras and compute such an isomorphism in the affirrmative case. We also provide algorithms for determining algebraic…