Related papers: Computing optimal shortcuts for networks
We consider the problem of choosing Euclidean points to maximize the sum of their weighted pairwise distances, when each point is constrained to a ball centered at the origin. We derive a dual minimization problem and show strong duality…
We propose a new algorithm that uses an auxiliary neural network to express the potential of the optimal transport map between two data distributions. In the sequel, we use the aforementioned map to train generative networks. Unlike WGANs,…
Shortest paths in complex networks play key roles in many applications. Examples include routing packets in a computer network, routing traffic on a transportation network, and inferring semantic distances between concepts on the World Wide…
We initiate the study of a fundamental combinatorial problem: Given a capacitated graph $G=(V,E)$, find a shortest walk ("route") from a source $s\in V$ to a destination $t\in V$ that includes all vertices specified by a set…
In this short paper, we present an improved algorithm for approximating the minimum cut on distributed (CONGEST) networks. Let $\lambda$ be the minimum cut. Our algorithm can compute $\lambda$ exactly in…
We study the network pricing problem where the leader maximizes their revenue by determining the optimal amounts of tolls to charge on a set of arcs, under the assumption that the followers will react rationally and choose the shortest…
Parametric optimization solves a family of optimization problems as a function of parameters. It is a critical component in situations where optimal decision making is repeatedly performed for updated parameter values, but computation…
We study the min-cost seed selection problem in online social networks, where the goal is to select a set of seed nodes with the minimum total cost such that the expected number of influenced nodes in the network exceeds a predefined…
The shortest path problem is related to many dynamic processes on networks, ranging from routing in communication networks to signaling in molecular interaction networks. When the network is fully known, the shortest path problem can be…
Spatial networks are a powerful framework for studying a large variety of systems belonging to a broad diversity of contexts: from transportation to biology, from epidemiology to communications, and migrations, to cite a few. Spatial…
We study an optimal control problem aimed at achieving a desired tradeoff between the network coherence and communication requirements in the distributed controller. Our objective is to add a certain number of edges to an undirected…
Problem of finding 2D paths of special shape, e.g. paths comprised of line segments having the property that the angle between any two consecutive segments does not exceed the predefined threshold, is considered in the paper. This problem…
For a set $Q$ of points in the plane and a real number $\delta \ge 0$, let $\mathbb{G}_\delta(Q)$ be the graph defined on $Q$ by connecting each pair of points at distance at most $\delta$. We consider the connectivity of…
In this paper, we consider the resource allocation problem in a network with a large number of connections which are used by a huge number of users. The resource allocation problem under discussion is a maximization problem with linear…
Given a set of sources and a set of sinks as points in the Euclidean plane, a directed network is a directed graph drawn in the plane with a directed path from each source to each sink. Such a network may contain nodes other than the given…
We propose an algorithm for distributed optimization over time-varying communication networks. Our algorithm uses an optimized ratio between the number of rounds of communication and gradient evaluations to achieve fast convergence. The…
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…
We show a deterministic constant-time local algorithm for constructing an approximately maximum flow and minimum fractional cut in multisource-multitarget networks with bounded degrees and bounded edge capacities. Locality means that the…
We investigate by numerical simulation and finite-size analysis the impact of long-range shortcuts on a spatially embedded transportation network. Our networks are built from two-dimensional ($d=2$) square lattices to be improved by the…
Although recovering an Euclidean distance matrix from noisy observations is a common problem in practice, how well this could be done remains largely unknown. To fill in this void, we study a simple distance matrix estimate based upon the…