相关论文: Remarks on d-Dimensional TSP Optimal Tour Length B…

Evolving diverse sets of high quality solutions has gained increasing interest in the evolutionary computation literature in recent years. With this paper, we contribute to this area of research by examining evolutionary diversity…

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…

Dynamical properties of lattice systems with long-range pair interactions, decaying like 1/r^{\alpha} with the distance r, are investigated, in particular the time scales governing the relaxation to equilibrium. Upon varying the interaction…

We consider the time-dependent traveling salesman problem (TDTSP), a generalization of the asymmetric traveling salesman problem (ATSP) to incorporate time-dependent cost functions. In our model, the costs of an arc can change arbitrarily…

We introduce the Observation Route Problem ($\textsf{ORP}$) defined as follows: Given a set of $n$ pairwise disjoint compact regions in the plane, find a shortest tour (route) such that an observer walking along this tour can see (observe)…

This work presents a tensor-network formulation of the Traveling Salesman Problem (TSP) and several of its variants. The approach represents candidate tours with tensor-network layers, weights them by Boltzmann factors, and enforces…

We propose a mechanism for calculating anomalous dimensions of higher-spin twist-two operators in N=4 SYM. We consider the ratio of the two-point functions of the operators and of their superconformal descendants or, alternatively, of the…

We provide a spectrum of new theoretical insights and practical results for finding a Minimum Dilation Triangulation (MDT), a natural geometric optimization problem of considerable previous attention: Given a set $P$ of $n$ points in the…

We give a polynomial time, $(1+\epsilon)$-approximation algorithm for the traveling repairman problem (TRP) in the Euclidean plane and on weighted trees. This improves on the known quasi-polynomial time approximation schemes for these…

The Traveling Tournament Problem (TTP) is a hard but interesting sports scheduling problem inspired by Major League Baseball, which is to design a double round-robin schedule such that each pair of teams plays one game in each other's home…

In this paper, we present some properties of time optimal controls for linear ODEs with the ball-type control constraint. More precisely, for an optimal control, we build up an upper bound for the number of its switching points; show that…

For $z_1,z_2,z_3 \in \Z^n$, the \emph{tristance} $d_3(z_1,z_2,z_3)$ is a generalization of the $L_1$-distance on $\Z^n$ to a quantity that reflects the relative dispersion of three points rather than two. A tristance anticode $\cA_d$ of…

The Metric Traveling Salesman Problem (TSP) is a classical NP-hard optimization problem. The double-tree shortcutting method for Metric TSP yields an exponentially-sized space of TSP tours, each of which approximates the optimal solution…

Euclidean spanners are important geometric structures, having found numerous applications over the years. Cornerstone results in this area from the late 80s and early 90s state that for any $d$-dimensional $n$-point Euclidean space, there…

We introduce and physically motivate the following problem in geometric combinatorics, originally inspired by analysing Bell inequalities. A grasshopper lands at a random point on a planar lawn of area one. It then jumps once, a fixed…

The Travelling Salesman Problem (TSP) is a classical combinatorial optimisation problem. Deep learning has been successfully extended to meta-learning, where previous solving efforts assist in learning how to optimise future optimisation…

Integration over curved manifolds with higher codimension and, separately, discrete variants of continuous operators, have been two important, yet separate themes in harmonic analysis, discrete geometry and analytic number theory research.…

Recently we derived a nonlinear U-spin amplitude relation for $D^0\to P^+P^-$, $P=\pi, K$, predicted to hold up to fourth order U-spin breaking terms of order $10^{-3}$. Here we study a similar relation for $D^0\to V^+P^-, V =\rho,…

We study the high-dimensional uniform prudent self-avoiding walk, which assigns equal probability to all nearest-neighbor self-avoiding paths of a fixed length that respect the prudent condition, namely, the path cannot take any step in the…

We evaluate the limit distribution of the maximal excursion of a random walk in any dimension for homogeneous environments and for self-similar supports under the assumption of spherical symmetry. This distribution is obtained in closed…