Related papers: Minimizing the Continuous Diameter when Augmenting…
For fixed $h \geq 2$, we consider the task of adding to a graph $G$ a set of weighted shortcut edges on the same vertex set, such that the length of a shortest $h$-hop path between any pair of vertices in the augmented graph is exactly the…
In this article, we propose a growing network model based on an optimal policy involving both topological and geographical measures. In this model, at each time step, a new node, having randomly assigned coordinates in a $1 \times 1$…
To address growth challenges facing large Data Centers and supercomputing clusters a new construction is presented for scalable, high throughput, low latency networks. The resulting networks require 1.5-5 times fewer switches, 2-6 times…
Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…
The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network…
Classical multidimensional scaling only works well when the noisy distances observed in a high dimensional space can be faithfully represented by Euclidean distances in a low dimensional space. Advanced models such as Maximum Variance…
A shortest-path algorithm finds a path containing the minimal cost between two vertices in a graph. A plethora of shortest-path algorithms is studied in the literature that span across multiple disciplines. This paper presents a survey of…
The energy landscape of high-dimensional non-convex optimization problems is crucial to understanding the effectiveness of modern deep neural network architectures. Recent works have experimentally shown that two different solutions found…
One of the most intriguing findings in the structure of neural network landscape is the phenomenon of mode connectivity: For two typical global minima, there exists a path connecting them without barrier. This concept of mode connectivity…
In the d-Euclidean Distance Matrix Completion (d-EDMC) problem, one aims to determine whether a given partial matrix of pairwise distances can be extended to a full Euclidean distance matrix in d dimensions. This problem is a cornerstone of…
The minimum and maximum cuts of an undirected edge-weighted graph are classic problems in graph theory. While the Min-Cut Problem can be solved in P, the Max-Cut Problem is NP-Complete. Exact and heuristic methods have been developed for…
In this paper we give fast distributed graph algorithms for detecting and listing small subgraphs, and for computing or approximating the girth. Our algorithms improve upon the state of the art by polynomial factors, and for girth, we…
Many real-world complex systems can be modeled as multiplex networks, where each layer represents a distinct set of interactions among the same entities. Controlling such systems-steering them toward desired states using external inputs-is…
We study the asymptotic growth of the diameter of a graph obtained by adding sparse "long" edges to a square box in $\Z^d$. We focus on the cases when an edge between $x$ and $y$ is added with probability decaying with the Euclidean…
For a graph $G$ spanning a metric space, the dilation of a pair of points is the ratio of their distance in the shortest path graph metric to their distance in the metric space. Given a graph $G$ and a budget $k$, a classic problem is to…
We analyze recurrent neural networks with diagonal hidden-to-hidden weight matrices, trained with gradient descent in the supervised learning setting, and prove that gradient descent can achieve optimality \emph{without} massive…
In this paper, we present two approximation algorithms for the directed multi-multiway cut and directed multicut problems. The so called region growing paradigm \cite{1} is modified and used for these two cut problems on directed graphs. By…
We initiate the algorithmic study of retracting a graph into a cycle in the graph, which seeks a mapping of the graph vertices to the cycle vertices, so as to minimize the maximum stretch of any edge, subject to the constraint that the…
Given a polygon representing a transportation network together with a point p in its interior, we aim to extend the network by inserting a line segment, called a feed-link, which connects p to the boundary of the polygon. Once a feed link…
The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the…