Related papers: On the Solution of Graph Isomorphism by Dynamical …
We introduce and study the problem of optimizing arbitrary functions over degree sequences of hypergraphs and multihypergraphs. We show that over multihypergraphs the problem can be solved in polynomial time. For hypergraphs, we show that…
Building on recent progress at the intersection of combinatorial optimization and deep learning, we propose an end-to-end trainable architecture for deep graph matching that contains unmodified combinatorial solvers. Using the presence of…
In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain property. For example, the Cluster…
In this paper, we show the existence of a polynomial time graph isomorphism algorithm for all graphs excluding graphs that are locally trianglefree. This particular class of graphs allows to divide the graph into neighbourhood sub-graph…
We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set…
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…
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 dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…
Graphs are widely used to model complicated data semantics in many application domains. In this paper, two novel and efficient algorithms Fast-ON and Fast-P are proposed for solving the subgraph isomorphism problem. The two algorithms are…
In this work we provide a novel approach for computing the coefficients of the characteristic polynomial of a square matrix. We demonstrate that each coefficient can be efficiently represented by a set of circle graphs. Thus, one can employ…
Data-driven approaches have been proven effective in solving combinatorial optimization problems over graphs such as the traveling salesman problems and the vehicle routing problem. The rationale behind such methods is that the input…
Graph clustering is a fundamental technique in data analysis with applications in many different fields. While there is a large body of work on clustering undirected graphs, the problem of clustering directed graphs is much less understood.…
It is unknown whether two graphs can be tested for isomorphism in polynomial time. A classical approach to the Graph Isomorphism Problem is the d-dimensional Weisfeiler-Lehman algorithm. The d-dimensional WL-algorithm can distinguish many…
We investigate novel random graph embeddings that can be computed in expected polynomial time and that are able to distinguish all non-isomorphic graphs in expectation. Previous graph embeddings have limited expressiveness and either cannot…
This paper discusses the graph covering problem in which a set of edges in an edge- and node-weighted graph is chosen to satisfy some covering constraints while minimizing the sum of the weights. In this problem, because of the large…
Polynomial systems occur in many fields of science and engineering. Polynomial homotopy continuation methods apply symbolic-numeric algorithms to solve polynomial systems. We describe the design and implementation of our web interface and…
Many hard combinatorial problems can be modeled by a system of polynomial equations. N. Alon coined the term polynomial method to describe the use of nonlinear polynomials when solving combinatorial problems. We continue the exploration of…
Dynamic graph algorithms have seen significant theoretical advancements, but practical evaluations often lag behind. This work bridges the gap between theory and practice by engineering and empirically evaluating recently developed…
This paper studies the fundamental problem of graph coloring in fully dynamic graphs. Since the problem of computing an optimal coloring, or even approximating it to within $n^{1-\epsilon}$ for any $\epsilon > 0$, is NP-hard in static…
Graph coarsening is a widely used dimensionality reduction technique for approaching large-scale graph machine learning problems. Given a large graph, graph coarsening aims to learn a smaller-tractable graph while preserving the properties…