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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…
This paper considers continuously differentiable functions of two vector variables that have (possibly a continuum of) min-max saddle points. We study the asymptotic convergence properties of the associated saddle-point dynamics…
The effect of fluctuations on the transport and thermodynamic properties of two-dimensional superconductors in a magnetic field is studied at low temperature. The fluctuation conductivity is calculated in the framework of the perturbation…
The traveling salesman (or salesperson) problem, short TSP, is a problem of strong interest to many researchers from mathematics, economics, and computer science. Manifold TSP variants occur in nearly every scientific field and application…
We study a driven zero range process which models a closed system of attractive particles that hop with site-dependent rates and whose steady state shows a condensation transition with increasing density. We characterise the dynamical…
The Traveling Salesman Problem is one of the most intensively studied combinatorial optimization problems due both to its range of real-world applications and its computational complexity. When combined with the Set Covering Problem, it…
Traveling salesman problem is a NP-hard problem. Until now, researchers have not found a polynomial time algorithm for traveling salesman problem. Among the existing algorithms, dynamic programming algorithm can solve the problem in time…
The Traveling Salesman Problem (TSP) is one of the classic and hard problems in combinatorial optimization. We develop a new heuristic that uses a connection between Minimum Cost Flow Problems and the TSP to improve on a given suboptimal…
In this case study, the renowned Travelling Salesmen problem has been studied. Travelling Salesman problem is a most demanding computational problem in Computer Science. The Travelling Salesmen problem has been solved by two different ways…
In this work we revisit the Hopfield-Tank algorithm for the traveling salesman problem (TSP) and report encouraging results, with a different dynamics, that makes the algorithm more efficient finding better solutions in much less…
We show that the traveling salesman problem (TSP) and its many variants may be modeled as functional optimization problems over a graph. In this formulation, all vertices and arcs of the graph are functionals; i.e., a mapping from a space…
When driving a disordered elastic manifold through quenched disorder, the pinning forces exerted on the center of mass are fluctuating, with mean $f_c=-\overline{F_w} $ and variance $\Delta(w)=\overline{F_w F_0}^c$, where $w$ is the…
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…
For some weighted $NP$-complete problems, checking whether a proposed solution is optimal is a non-trivial task. Such is the case for the celebrated traveling salesman problem, or the spin-glass problem in 3 dimensions. In this letter, we…
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 study the traveling salesman problem when the positions of the…
The Travelling Salesman Problem (TSP) is a well known and challenging combinatorial optimisation problem. Its computational intractability has attracted a number of heuristic approaches to generate satisfactory, if not optimal, candidate…
Traditionally, it is understood that fluctuations in the equilibrium distribution are not evident in thermodynamic systems of large $N$ (the number of particles in the system) \cite{Huang1}. In this paper we examine the validity of this…
The zero temperature localization of interacting electrons coupled to a two-dimensional quenched random potential, and constrained to move on a fluctuating one-dimensional string embedded in the disordered plane, is studied using a…
We point out that the low temperature saturation of the electron phase decoherence time in a disordered conductor can be explained within the existing theory of weak localization provided the effect of quantum (high frequency) fluctuations…
The traveling salesman problem (TSP) is a fundamental problem in combinatorial optimization. Several semidefinite programming relaxations have been proposed recently that exploit a variety of mathematical structures including, e.g.,…