Related papers: A polynomial time iterative algorithm for matching…
Graph matching aims at finding the vertex correspondence between two unlabeled graphs that maximizes the total edge weight correlation. This amounts to solving a computationally intractable quadratic assignment problem. In this paper we…
We provide linear-time algorithms for geometric graphs with sublinearly many crossings. That is, we provide algorithms running in O(n) time on connected geometric graphs having n vertices and k crossings, where k is smaller than n by an…
We present a new approach for solving (minimum disagreement) correlation clustering that results in sublinear algorithms with highly efficient time and space complexity for this problem. In particular, we obtain the following algorithms for…
Graph matching problem aims to identify node correspondence between two or more correlated graphs. Previous studies have primarily focused on models where only edge information is provided. However, in many social networks, not only the…
Let $H$ be a $k$-graph on $n$ vertices, with minimum codegree at least $n/k + cn$ for some fixed $c > 0$. In this paper we construct a polynomial-time algorithm which finds either a perfect matching in $H$ or a certificate that none exists.…
In the Exact Matching problem, we are given a graph whose edges are colored red or blue and the task is to decide for a given integer k, if there is a perfect matching with exactly k red edges. Since 1987 it is known that the Exact Matching…
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…
For two independent Erd\H{o}s-R\'enyi graphs $\mathbf G(n,p)$, we study the maximal overlap (i.e., the number of common edges) of these two graphs over all possible vertex correspondence. We present a polynomial-time algorithm which finds a…
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
The $k$-cut problem asks, given a connected graph $G$ and a positive integer $k$, to find a minimum-weight set of edges whose removal splits $G$ into $k$ connected components. We give the first polynomial-time algorithm with approximation…
Graph alignment aims at finding the vertex correspondence between two correlated graphs, a task that frequently occurs in graph mining applications such as social network analysis. Attributed graph alignment is a variant of graph alignment,…
In this paper, we study the problem of recovering the latent vertex correspondence between two correlated random graphs with vastly inhomogeneous and unknown edge probabilities between different pairs of vertices. Inspired by and extending…
We propose a consistent polynomial-time method for the unseeded node matching problem for networks with smooth underlying structures. Despite widely conjectured by the research community that the structured graph matching problem to be…
Random graph matching refers to recovering the underlying vertex correspondence between two random graphs with correlated edges; a prominent example is when the two random graphs are given by Erd\H{o}s-R\'{e}nyi graphs $G(n,\frac{d}{n})$.…
Gaussian graphical models are of great interest in statistical learning. Because the conditional independencies between different nodes correspond to zero entries in the inverse covariance matrix of the Gaussian distribution, one can learn…
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…
In a seminal paper on finding large matchings in sparse random graphs, Karp and Sipser proposed two algorithms for this task. The second algorithm has been intensely studied, but due to technical difficulties, the first algorithm has…
We study the problem of recovering the structure underlying large Gaussian graphical models or, more generally, partial correlation graphs. In high-dimensional problems it is often too costly to store the entire sample covariance matrix. We…
We describe a new algorithm for Gaussian Elimination suitable for general (unsymmetric and possibly singular) sparse matrices, of any entry type, which has a natural parallel and distributed-memory formulation but degrades gracefully to…
In this paper, the problem of matching pairs of correlated random graphs with multi-valued edge attributes is considered. Graph matching problems of this nature arise in several settings of practical interest including social network…