Related papers: Impossibility of Partial Recovery in the Graph Ali…
In this paper we propose a method of proving impossibility results based on applying strong data-processing inequalities to estimate mutual information between sets of variables forming certain Markov random fields. The end result is that…
Graph matching is a fruitful area in terms of both algorithms and theories. In this paper, we exploit the degree information, which was previously used only in noiseless graphs and perfectly-overlapping Erd\H{o}s--R\'enyi random graphs…
This paper concerns the large deviations of a system of interacting particles on a random graph. There is no stochasticity, and the only sources of disorder are the random graph connections, and the initial condition. The average number of…
We propose an efficient algorithm for matching two correlated Erd\H{o}s--R\'enyi graphs with $n$ vertices whose edges are correlated through a latent vertex correspondence. When the edge density $q= n^{- \alpha+o(1)}$ for a constant $\alpha…
The graph matching problem emerges naturally in various applications such as web privacy, image processing and computational biology. In this paper, graph matching is considered under a stochastic model, where a pair of randomly generated…
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…
In this paper, we propose a family of label recovery problems on weighted Euclidean random graphs. The vertices of a graph are embedded in $\mathbb{R}^d$ according to a Poisson point process, and are assigned to a discrete community label.…
Detection of planted subgraphs in Erd\"os-R\'enyi random graphs has been extensively studied, leading to a rich body of results characterizing both statistical and computational thresholds. However, most prior work assumes a purely random…
We consider an inhomogeneous Erd\H{o}s-R\'enyi random graph ensemble with exponentially decaying random disconnection probabilities determined by an i.i.d. field of variables with heavy tails and infinite mean associated to the vertices of…
We consider sequences of large sparse random graphs whose degree distribution approaches a limit with finite mean. This model includes both the random regular graphs and the Erd\"os-Renyi graphs of constant average degree. We prove that the…
Subgraph isomorphism, also known as subgraph matching, is typically regarded as an NP-complete problem. This complexity is further compounded in practical applications where edge weights are real-valued and may be affected by measurement…
Given two Erd\H{o}s-R\'enyi graphs with $n$ vertices whose edges are correlated through a latent vertex correspondence, we study complexity lower bounds for the associated correlation detection problem for the class of low-degree polynomial…
Motivated by alignment of correlated sparse random graphs, we introduce a hypothesis testing problem of deciding whether or not two random trees are correlated. We obtain sufficient conditions under which this testing is impossible or…
Graph signal processing (GSP) provides a powerful framework for analyzing signals arising in a variety of domains. In many applications of GSP, multiple network structures are available, each of which captures different aspects of the same…
Suppose a graph $G$ is stochastically created by uniformly sampling vertices along a line segment and connecting each pair of vertices with a probability that is a known decreasing function of their distance. We ask if it is possible to…
In the sufficiently sparse case, we find the probability that a uniformly random bipartite graph with given degree sequence contains no edge from a specified set of edges. This enables us to enumerate loop-free digraphs and oriented graphs…
This paper builds theoretical foundations for the recovery of a newly proposed class of smooth graph signals, approximately bandlimited graph signals, under three sampling strategies: uniform sampling, experimentally designed sampling and…
The stable matching problem is a prototype model in economics and social sciences where agents act selfishly to optimize their own satisfaction, subject to mutually conflicting constraints. A stable matching is a pairing of adjacent…
Random geometric graphs are random graph models defined on metric measure spaces. A random geometric graph is generated by first sampling points from a metric space and then connecting each pair of sampled points independently with a…
A major question in the study of the Erd\H{o}s--R\'enyi random graph is to understand the probability that it contains a given subgraph. This study originated in classical work of Erd\H{o}s and R\'enyi (1960). More recent work studies this…