Related papers: From tree matching to sparse graph alignment
We investigate sublinear-time algorithms that take partially erased graphs represented by adjacency lists as input. Our algorithms make degree and neighbor queries to the input graph and work with a specified fraction of adversarial…
We consider the following stochastic matching problem on both weighted and unweighted graphs: A graph $G(V, E)$ along with a parameter $p \in (0, 1)$ is given in the input. Each edge of $G$ is realized independently with probability $p$.…
In this paper, assuming the low-degree conjecture, we provide evidence of computational hardness for two problems: (1) the (partial) matching recovery problem in the sparse correlated Erd\H{o}s-R\'enyi graphs $\mathcal G(n,q;\rho)$ when the…
We determine the sharp threshold for the containment of all $n$-vertex trees of bounded degree in random geometric graphs with $n$ vertices. This provides a geometric counterpart of Montgomery's threshold result for binomial random graphs,…
We consider random walks on random graphs, focusing on return probabilities and hitting times for sparse Erdos-Renyi graphs. Using the tree approach which is expected to be exact in the large graph limit, we show how to solve for the…
We consider the Backup Placement problem in networks in the $\mathcal{CONGEST}$ distributed setting. Given a network graph $G = (V,E)$, the goal of each vertex $v \in V$ is selecting a neighbor, such that the maximum number of vertices in…
Random $s$-intersection graphs have recently received considerable attention in a wide range of application areas. In such a graph, each vertex is equipped with a set of items in some random manner, and any two vertices establish an…
We introduce a random intersection graph process aimed at modeling sparse evolving affiliation networks that admit tunable (power law) degree distribution and assortativity and clustering coefficients. We show the asymptotic degree…
In 2007 we introduced a general model of sparse random graphs with independence between the edges. The aim of this paper is to present an extension of this model in which the edges are far from independent, and to prove several results…
An outerstring graph is the intersection graph of curves lying inside a disk with one endpoint on the boundary of the disk. We show that an outerstring graph with $n$ vertices has treewidth $O(\alpha\log n)$, where $\alpha$ denotes the…
We propose a new model, the Neighbor Mixture Model (NMM), for modeling node labels in a graph. This model aims to capture correlations between the labels of nodes in a local neighborhood. We carefully design the model so it could be an…
The graph edit distance is used for comparing graphs in various domains. Due to its high computational complexity it is primarily approximated. Widely-used heuristics search for an optimal assignment of vertices based on the distance…
Regression trees are one of the oldest forms of AI models, and their predictions can be made without a calculator, which makes them broadly useful, particularly for high-stakes applications. Within the large literature on regression trees,…
The Steiner tree problem aims to determine a minimum edge-weighted tree that spans a given set of terminal vertices from a given graph. In the past decade, a considerable number of algorithms have been developed to solve this…
Graph neural networks have been successful for machine learning, as well as for combinatorial and graph problems such as the Subgraph Isomorphism Problem and the Traveling Salesman Problem. We describe an approach for computing graph…
Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…
We make the first steps towards generalizing the theory of stochastic block models, in the sparse regime, towards a model where the discrete community structure is replaced by an underlying geometry. We consider a geometric random graph…
A combinatorial analysis of the false alarm (FA) and misdetection (MD) probabilities of non-adaptive group testing with sparse pooling graphs is developed. The analysis targets the combinatorial orthogonal matching pursuit and definite…
We propose a simple and efficient local algorithm for graph isomorphism which succeeds for a large class of sparse graphs. This algorithm produces a low-depth canonical labeling, which is a labeling of the vertices of the graph that…
Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved…