Related papers: Computing optimal shortcuts for networks
Finding shortest paths in a given network (e.g., a computer network or a road network) is a well-studied task with many applications. We consider this task under the presence of an adversary, who can manipulate the network by perturbing its…
We study a scenario for route planning in road networks, where the objective to be optimized may change between every shortest path query. Since this invalidates many of the known speedup techniques for road networks that are based on…
What is the dimension of a network? Here, we view it as the smallest dimension of Euclidean space into which nodes can be embedded so that pairwise distances accurately reflect the connectivity structure. We show that a recently proposed…
Network optimization has generally been focused on solving network flow problems, but recently there have been investigations into optimizing network characteristics. Optimizing network connectivity to maximize the number of nodes within a…
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…
Many distributed optimization algorithms achieve existentially-optimal running times, meaning that there exists some pathological worst-case topology on which no algorithm can do better. Still, most networks of interest allow for…
We study the following two maximization problems related to spanning trees in the Euclidean plane. It is not known whether or not these problems are NP-hard. We present approximation algorithms with better approximation ratios for both…
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…
Structural bias or segregation of networks refers to situations where two or more disparate groups are present in the network, so that the groups are highly connected internally, but loosely connected to each other. In many cases it is of…
Recently, In [Phys. Rev. Lett. 104, 018701 (2010)] the authors studied a spatial network which is constructed from a regular lattice by adding long-range edges (shortcuts) with probability $P_{ij}\sim r_{ij}^{-\alpha}$, where $r_{ij}$ is…
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…
We study a number of multi-route cut problems: given a graph G=(V,E) and connectivity thresholds k_(u,v) on pairs of nodes, the goal is to find a minimum cost set of edges or vertices the removal of which reduces the connectivity between…
Given a set of points in the plane, we want to establish a connection network between these points that consists of several disjoint layers. Motivated by sensor networks, we want that each layer is spanning and plane, and that no edge is…
Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to…
The minimal network problem is a classical topic in geometric measure theory and the calculus of variations, which aims to find networks of minimal length connecting given points. Most classical results are established in the Euclidean…
In established network architectures, shortcut connections are often used to take the outputs of earlier layers as additional inputs to later layers. Despite the extraordinary effectiveness of shortcuts, there remain open questions on the…
Numerical computation of shortest paths or geodesics on curved domains, as well as the associated geodesic distance, arises in a broad range of applications across digital geometry processing, scientific computing, computer graphics, and…
Two-stage methods addressing continuous shortest path problems start local minimization from discrete shortest paths in a spatial graph. The convergence of such hybrid methods to global minimizers hinges on the discretization error induced…
Segment Routing is a recent network technology that helps optimizing network throughput by providing finer control over the routing paths. Instead of routing directly from a source to a target, packets are routed via intermediate waypoints.…
The construction of $r$-nets offers a powerful tool in computational and metric geometry. We focus on high-dimensional spaces and present a new randomized algorithm which efficiently computes approximate $r$-nets with respect to Euclidean…