Related papers: Diffusive behavior of a greedy traveling salesman
We explore a two-step optimization problem in random environments, the so-called restaurant-coffee shop problem, where a walker aims at visiting the nearest and better restaurant in an area and then move to the nearest and better…
This paper investigates the problem of distributed network-wide averaging and proposes a new greedy gossip algorithm. Instead of finding the optimal path of each node in a greedy manner, the proposed approach utilises a suboptimal…
We study the full distribution $P_M(S)$ of the number of distinct sites $S$ visited by a random walker on a $d$-dimensional lattice after $M$ steps. We focus on the case $d \ge 2$, and we are interested in the long-time limit $M \gg 1$. Our…
We consider super-diffusive L\'evy walks in $d \geqslant 2$ dimensions when the duration of a single step, i.e., a ballistic motion performed by a walker, is governed by a power-law tailed distribution of infinite variance and finite mean.…
We have studied numerically the frequency distribution $\rho (n)$ of the n-th neighbour along the optimal tour in the Euclidean travelling salesman problem for N cities, in dimensions d=2 and d=3. We find there is no significant dependence…
From the gambling logs of an online lottery game we extract the probability distribution of various quantities (e.g., bet value, total pool size, waiting time between successive gambles) as well as related correlation coefficients. We view…
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…
Motivated by studies on the recurrent properties of animal and human mobility, we introduce a path-dependent random walk model with long range memory for which not only the mean square displacement (MSD) can be obtained exactly in the…
We investigate a L\'evy-Walk alternating between velocities $\pm v_0$ with opposite sign. The sojourn time probability distribution at large times is a power law lacking its mean or second moment. The first case corresponds to a ballistic…
We examine self-avoiding walks in dimensions 4 to 8 using high-precision Monte-Carlo simulations up to length N=16384, providing the first such results in dimensions $d > 4$ on which we concentrate our analysis. We analyse the scaling…
This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is…
A L\'evy random medium, in a given space, is a random point process where the distances between points, a.k.a. targets, are long-tailed. Random walks visiting the targets of a L\'evy random medium have been used to model many (physical,…
Random walks describe diffusion processes, where movement at every time step is restricted to only the neighbouring locations. We construct a quantum random walk algorithm, based on discretisation of the Dirac evolution operator inspired by…
Recent work on exploration in reinforcement learning (RL) has led to a series of increasingly complex solutions to the problem. This increase in complexity often comes at the expense of generality. Recent empirical studies suggest that,…
An efficient searcher needs to balance properly the tradeoff between the exploration of new spatial areas and the exploitation of nearby resources, an idea which is at the core of scale-free L\'evy search strategies. Here we study…
With applications to many disciplines, the traveling salesman problem (TSP) is a classical computer science optimization problem with applications to industrial engineering, theoretical computer science, bioinformatics, and several other…
We consider correlated L\'evy walks on a class of two- and three-dimensional deterministic self-similar structures, with correlation between steps induced by the geometrical distribution of regions, featuring different diffusion properties.…
This paper describes a simple greedy D-approximation algorithm for any covering problem whose objective function is submodular and non-decreasing, and whose feasible region can be expressed as the intersection of arbitrary (closed upwards)…
We prove a general result that if a Metropolis--Hastings algorithm has a proposal that is not geometrically ergodic and the acceptance rate approaches unity at a suitable rate as the state variable becomes large, then the Metropolised chain…
Solutions to Traveling salesman problem have been obtained with several algorithms. However, few of them has discussed about the statistical distribution of lengths for the quasi-optimal path obtained. For a random set of cities such a…