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The traveling salesman problem is one of the most studied combinatorial optimization problems, because of the simplicity in its statement and the difficulty in its solution. We characterize the optimal cycle for every convex and increasing…
We give a constant factor approximation algorithm for the asymmetric traveling salesman problem when the support graph of the solution of the Held-Karp linear programming relaxation has bounded orientable genus.
We study a new version of the Traveling Salesperson Problem, called \VectorTSP, where the traveler is subject to discrete acceleration constraints, as defined in the paper-and-pencil game Racetrack (also known as Vector Racer). In this…
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 a one dimensional lattice thermal fluctuations destroy the long-range order making particles of the lattice move on a scale much larger than the lattice spacing. We discuss the assumption that this motion may be responsible for the…
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…
The Colored Points Traveling Salesman Problem (Colored Points TSP) is introduced in this work as a novel variation of the traditional Traveling Salesman Problem (TSP) in which the set of points is partitioned into multiple classes, each of…
Discrete version of state transition algorithm is proposed in order to solve the traveling salesman problem. Three special operators for discrete optimization problem named swap, shift and symmetry transformations are presented. Convergence…
The traveling salesman problem (TSP) famously asks for a shortest tour that a salesperson can take to visit a given set of cities in any order. In this paper, we ask how much faster $k \ge 2$ salespeople can visit the cities if they divide…
This article proposes the first known algorithm that achieves a constant-factor approximation of the minimum length tour for a Dubins' vehicle through $n$ points on the plane. By Dubins' vehicle, we mean a vehicle constrained to move at…
In this paper we propose some novel path planning strategies for a double integrator with bounded velocity and bounded control inputs. First, we study the following version of the Traveling Salesperson Problem (TSP): given a set of points…
There are many ways of establishing upper bounds on fluctuations of random variables, but there is no systematic approach for lower bounds. As a result, lower bounds are unknown in many important problems. This paper introduces a general…
Electron transport through amorphous monatomic metallic structures generated earlier by molecular dynamics simulations is studied numerically. The interference of electronic trajectories backscattered by the structural disorder probes the…
The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly…
The standard LP relaxation of the asymmetric traveling salesman problem has been conjectured to have a constant integrality gap in the metric case. We prove this conjecture when restricted to shortest path metrics of node-weighted digraphs.…
We study thermal fluctuation corrections to charge and heat conductivity in systems with locally conserved energy and charge, but without locally conserved momentum. Thermal fluctuations may naturally lead to a lower bound on diffusion…
It is argued that the (traditional) global level statistics which determines localization and coherent transport properties of disordered systems at zero temperature (e.g. the Anderson model) becomes inappropriate when it comes to…
A Langevin equation whose deterministic part undergoes a saddle-node bifurcation is investigated theoretically. It is found that statistical properties of relaxation trajectories in this system exhibit divergent behaviors near a saddle-node…
This is a study of phase-coherent conduction through a ballistic point contact with disordered leads. The disorder imposes mesoscopic (sample-to-sample) fluctuations and weak-localization corrections on the conductance, and also leads to…
We establish sharp well-posedness and approximation estimates for variational saddle point systems at the continuous level. The main results of this note have been known to be true only in the finite dimensional case. Known spectral results…