Related papers: Trajectory stability in the traveling salesman pro…
In the traveling salesman problem, one must find the length of the shortest closed tour visiting given ``cities''. We study the stochastic version of the problem, taking the locations of cities and the distances separating them to be random…
An important variant of the classic Traveling Salesman Problem (TSP) is the Dynamic TSP, in which a system with dynamic constraints is tasked with visiting a set of n target locations (in any order) in the shortest amount of time. Such…
We propose a learning algorithm for solving the traveling salesman problem based on a simple strategy of trial and adaptation: i) A tour is selected by choosing cities probabilistically according to the ``synaptic'' strengths between…
In this paper we study a property of time-dependent graphs, dubbed path ranking invariance. Broadly speaking, a time-dependent graph is path ranking invariant if the ordering of its paths (w.r.t. travel time) is independent of the start…
Any collection can be ranked. Sports and games are common examples of ranked systems: players and teams are constantly ranked using different methods. The statistical properties of rankings have been studied for almost a century in a…
How do decisions change with the economic environment and with time? This paper studies general nonstationary stopping problems and provides the methodological tools to answer these questions. First, we identify conditions that ensure a…
Consider the Euclidean traveling salesman problem with $n$ random points on the plane. Suppose that one of the points is shifted to a new random location. This gives us a new optimal path. Consider such shifts for each of the $n$ points. Do…
The study of the dynamic behavior of cross-sectional ranks over time for functional data and the ranks of the observed curves at each time point and their temporal evolution can yield valuable insights into the time dynamics of functional…
This paper considers theoretical solutions for path planning problems under non-probabilistic uncertainty used in the travel salesman problems under uncertainty. The uncertainty is on the paths between the cities as nodes in a travelling…
We propose that the statistics of the optimal tour in the planar random Euclidean traveling salesman problem is conformally invariant on large scales. This is exhibited in power-law behavior of the probabilities for the tour to zigzag…
Virtually anything can be and is ranked; people, institutions, countries, words, genes. Rankings reduce complex systems to ordered lists, reflecting the ability of their elements to perform relevant functions, and are being used from…
Because of the complexity of urban transportation networks and the temporal changes in traffic conditions, it is difficult to assess real-time traffic situations. However, the development of information terminals has made it easier to…
In empirical studies of random walks, continuous trajectories of animals or individuals are usually sampled over a finite number of points in space and time. It is however unclear how this partial observation affects the measured…
We extend a previous statistical mechanical treatment of the traveling salesman problem by defining a discrete "site disordered'' problem in which fluctuations about saddle points can be computed. The results clarify the basis of our…
Stability of Wardrop equilibria is analyzed for dynamical transportation networks in which the drivers' route choices are influenced by information at multiple temporal and spatial scales. The considered model involves a continuum of…
We consider a variation of the well-known traveling salesman problem in which there are multiple agents who all have to tour the whole set of nodes of the same graph, while obeying node- and edge-capacity constraints require that agents…
We study the random link traveling salesman problem, where lengths l_ij between city i and city j are taken to be independent, identically distributed random variables. We discuss a theoretical approach, the cavity method, that has been…
This paper considers the use of recently proposed optimal transport-based multivariate test statistics, namely rank energy and its variant the soft rank energy derived from entropically regularized optimal transport, for the unsupervised…
This work examines the phenomenon of path variability in urban navigation, where small changes in destination might lead to significantly different suggested routes. Starting from an observation of this variability over the city of…
Constant-factor, polynomial-time approximation algorithms are presented for two variations of the traveling salesman problem with time windows. In the first variation, the traveling repairman problem, the goal is to find a tour that visits…