Related papers: Hyperfinite graphings and combinatorial optimizati…
An isomorphism between two graphs is a bijection between their vertices that preserves the edges. We consider the problem of determining whether two finite undirected weighted graphs are isomorphic, and finding an isomorphism relating them…
Graph matching---aligning a pair of graphs to minimize their edge disagreements---has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and…
Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…
We extend the concept of the law of a finite graph to graphings, which are, in general, infinite graphs whose vertices are equipped with the structure of a probability space. By doing this, we obtain a vast array of new unimodular measures.…
Graphs provide an efficient tool for object representation in various computer vision applications. Once graph-based representations are constructed, an important question is how to compare graphs. This problem is often formulated as a…
Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…
The design of good heuristics or approximation algorithms for NP-hard combinatorial optimization problems often requires significant specialized knowledge and trial-and-error. Can we automate this challenging, tedious process, and learn the…
We introduce a relaxation for homomorphism problems that combines semidefinite programming with linear Diophantine equations, and propose a framework for the analysis of its power based on the spectral theory of association schemes. We use…
Topological mapping of a large physical system on a graph, and its decomposition using universal measures is proposed. We find inherent limits to the potential for optimization of a given system and its approximate representations by…
The graph isomorphism problem looks deceptively simple, but although polynomial-time algorithms exist for certain types of graphs such as planar graphs and graphs with bounded degree or eigenvalue multiplicity, its complexity class is still…
The maximization for the independence systems defined on graphs is a generalization of combinatorial optimization problems such as the maximum $b$-matching, the unweighted MAX-SAT, the matchoid, and the maximum timed matching problems. In…
We suggest a reduction of the combinatorial problem of hypergraph partitioning to a continuous optimization problem.
Exploring the power of linear programming for combinatorial optimization problems has been recently receiving renewed attention after a series of breakthrough impossibility results. From an algorithmic perspective, the related questions…
We present recent advances in harmonic analysis on infinite graphs. Our approach combines combinatorial tools with new results from the theory of unbounded Hermitian operators in Hilbert space, geometry, boundary constructions, and spectral…
Inspired by notorious combinatorial optimization problems on graphs, in this paper we consider a series of related problems defined using a metric space and topology determined by a graph. Particularly, we present the Independent Set,…
This paper introduces a discrete relaxation for the class of combinatorial optimization problems which can be described by a set partitioning formulation under packing constraints. We present two combinatorial relaxations based on computing…
We relate the graph isomorphism problem to the solvability of certain systems of linear equations with nonnegative variables. This version replaces the two previous versions of this paper.
Packing problems in discrete geometry can be modeled as finding independent sets in infinite graphs where one is interested in independent sets which are as large as possible. For finite graphs one popular way to compute upper bounds for…
We prove measurable analogues of Whitney's classical theorems on weak isomorphisms of finite graphs. In the setting of locally finite graphings, we introduce a notion of weak isomorphism as an edge-measure-preserving Borel bijection that…
We characterize hyperfinite bipartite graphings that admit measurable perfect matchings. In particular, we prove that every regular hyperfinite bipartite graphing admits a measurable perfect matching if it is one-ended or the degree is odd.…