Related papers: Designing optimal transport networks
We seek to augment a geometric network in the Euclidean plane with shortcuts to minimize its continuous diameter, i.e., the largest network distance between any two points on the augmented network. Unlike in the discrete setting where a…
Transport in complex networks can describe a variety of natural and human-engineered processes including biological, societal and technological ones. However, how the properties of the source and drain nodes can affect transport subject to…
One of the most important features of spatial networks such as transportation networks, power grids, Internet, neural networks, is the existence of a cost associated with the length of links. Such a cost has a profound influence on the…
Modeling traffic distribution and extracting optimal flows in multilayer networks is of utmost importance to design efficient multi-modal network infrastructures. Recent results based on optimal transport theory provide powerful and…
We propose an approach based on analysis of cost-quality tradeoffs for comparison of efficiency of various algorithms for small-world network construction. A number of both known in the literature and original algorithms for complex…
One of the challenges for future infrastructures is how to design a network with high efficiency and strong connectivity at low cost. We propose self-organized geographical networks beyond the vulnerable scale-free structure found in many…
This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex…
This paper studies online shortest path routing over multi-hop networks. Link costs or delays are time-varying and modeled by independent and identically distributed random processes, whose parameters are initially unknown. The parameters,…
We study the problem of computing all Pareto-optimal journeys in a public transit network regarding the two criteria of arrival time and number of transfers taken. In recent years, great advances have been made in making public transit…
We model the formation of multi-layer transportation networks as a multi-objective optimization process, where service providers compete for passengers, and the creation of routes is determined by a multi-objective cost function encoding a…
We present an algorithm for optimal guidance of users in road networks. It is a "stochastic-on-time-arrival (SOTA)"-like algorithm which calculates optimal guidance strategies with reliable paths, for road network origin-destination pairs.…
We develop Brenier theorems on iterated Wasserstein spaces. For a separable Hilbert space $H$ and $N\geq 1$, we construct a full-support probability $\Lambda$ on $P_2^{N}(H)= P_2(... P_2(H)...)$ that is transport regular: for every $Q$ with…
We consider the problem of constructing a communication infrastructure from scratch, for a collection of identical wireless nodes. Combinatorially, this means a) finding a set of links that form a strongly connected spanning graph on a set…
Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be…
We present a novel heuristic algorithm for routing optimization on complex networks. Previously proposed routing optimization algorithms aim at avoiding or reducing link overload. Our algorithm balances traffic on a network by minimizing…
In the regime of bounded transportation costs, additive approximations for the optimal transport problem are reduced (rather simply) to relative approximations for positive linear programs, resulting in faster additive approximation…
As part of the effort undertaken to understand urban environments and their generation, we need to explore models that produce statistically valid configurations of roads. These sort of models will help us to derive plausible mechanisms for…
This paper studies the trajectory optimization problem in a scenario where a single rotary-wing UAV acts as a relay of data payloads for downlink transmission requests generated randomly by two ground nodes (GNs) in a wireless network. The…
This chapter provides a comprehensive and self-contained discussion of the most recent developments of information theory of networks. Maximum entropy models of networks are the least biased ensembles enforcing a set of constraints and are…
Transport is an important function of networks. Studying transport efficiency sheds light on the dynamic processes occurring within various underlying structures and offers a wide range of applications. To construct networks with different…