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We present a simple nonadaptive randomized algorithm that estimates the number of edges in a simple, unweighted, undirected graph, possibly containing isolated vertices, using only degree and random edge queries. For an $n$-vertex graph,…
Let G = (V, E) be a directed and weighted graph with vertex set V of size n and edge set E of size m, such that each edge (u, v) \in E has a real-valued weight w(u, c). An arborescence in G is a subgraph T = (V, E') such that for a vertex u…
Direct image-to-graph transformation is a challenging task that involves solving object detection and relationship prediction in a single model. Due to this task's complexity, large training datasets are rare in many domains, making the…
In this work, we propose an end-to-end graph network that learns forward and inverse models of particle-based physics using interpretable inductive biases. Physics-informed neural networks are often engineered to solve specific problems…
Theoretical and empirical evidence indicates that the depth of neural networks is crucial for their success. However, training becomes more difficult as depth increases, and training of very deep networks remains an open problem. Here we…
In the Properly Colored Spanning Tree problem, we are given an edge-colored undirected graph and the goal is to find a properly colored spanning tree, i.e., a spanning tree in which any two adjacent edges have distinct colors. The problem…
Experimental validation of chemical processes is slow and costly, limiting exploration in materials discovery. Machine learning can prioritize promising candidates, but existing data in patents and literature is heterogeneous and difficult…
This paper studies graphical model selection, i.e., the problem of estimating a graph of statistical relationships among a collection of random variables. Conventional graphical model selection algorithms are passive, i.e., they require all…
Say that an edge of a graph G dominates itself and every other edge adjacent to it. An edge dominating set of a graph G = (V,E) is a subset of edges E' of E which dominates all edges of G. In particular, if every edge of G is dominated by…
In this paper, learning of tree-structured Gaussian graphical models from distributed data is addressed. In our model, samples are stored in a set of distributed machines where each machine has access to only a subset of features. A central…
A (Euclidean) greedy drawing of a graph is a drawing in which, for any two vertices $s,t$ ($s \neq t$), there is a neighbor vertex of $s$ that is closer to $t$ than to $s$ in the Euclidean distance. Greedy drawings are important in the…
Recent advances in deep learning have made it possible to quantify urban metrics at fine resolution, and over large extents using street-level images. Here, we focus on measuring urban tree cover using Google Street View (GSV) images.…
We consider the problem of learning the weighted edges of a balanced mixture of two undirected graphs from epidemic cascades. While mixture models are popular modeling tools, algorithmic development with rigorous guarantees has lagged.…
We introduce an exact distributed algorithm to train Random Forest models as well as other decision forest models without relying on approximating best split search. We explain the proposed algorithm and compare it to related approaches for…
An EPG-representation of a graph $G$ is a collection of paths in a plane square grid, each corresponding to a single vertex of $G$, so that two vertices are adjacent if and only if their corresponding paths share infinitely many points. In…
Recently similarity graphs became the leading paradigm for efficient nearest neighbor search, outperforming traditional tree-based and LSH-based methods. Similarity graphs perform the search via greedy routing: a query traverses the graph…
Graph transformation systems have the potential to be realistic models of chemistry, provided a comprehensive collection of reaction rules can be extracted from the body of chemical knowledge. A first key step for rule learning is the…
A classical enumerative result states that, given a graph $G$ and a vertex $u$, the number of connected subgraphs of $G$ is equal to the number of orientations of $G$ such that every vertex can reach $u$ by a directed path. We show that…
Graph matching can be formalized as a combinatorial optimization problem, where there are corresponding relationships between pairs of nodes that can be represented as edges. This problem becomes challenging when there are potential…
A tree with at most k leaves is called k-ended tree, and a tree with exactly k leaves is called k-end tree, where a leaf is a vertex of degree one. Contraction of a graph G along the edge e means deleting the edge e and identifying its end…