scholarly journals An upper bound for the length of a traveling salesman path in the Heisenberg group

2016 ◽  
Vol 32 (2) ◽  
pp. 391-417 ◽  
Author(s):  
Sean Li ◽  
Raanan Schul
Keyword(s):  
Heisenberg Group ◽  
Upper Bound ◽  
Traveling Salesman ◽  
Traveling Salesman Path

scholarly journals Traveling salesman path problems

2006 ◽  
Vol 113 (1) ◽  
pp. 39-59 ◽  
Author(s):  
Fumei Lam ◽  
Alantha Newman
Keyword(s):  
Traveling Salesman ◽  
Traveling Salesman Path

scholarly journals The asymmetric traveling salesman path LP has constant integrality ratio

2019 ◽  
Vol 183 (1-2) ◽  
pp. 379-395 ◽  
Author(s):  
Anna Köhne ◽  
Vera Traub ◽  
Jens Vygen
Keyword(s):  
Traveling Salesman ◽  
Traveling Salesman Path

scholarly journals New Bounds for the Traveling Salesman Constant

2015 ◽  
Vol 47 (01) ◽  
pp. 27-36 ◽  
Author(s):  
Stefan Steinerberger
Keyword(s):  
Lower Bounds ◽  
Random Variables ◽  
Universal Constant ◽  
Traveling Salesman ◽  
Upper And Lower Bounds ◽  
Unit Square ◽  
Traveling Salesman Path

Let X 1, X 2, …, X n be independent and uniformly distributed random variables in the unit square [0, 1]2, and let L(X 1, …, X n ) be the length of the shortest traveling salesman path through these points. In 1959, Beardwood, Halton and Hammersley proved the existence of a universal constant β such that lim n→∞ n −1/2 L(X 1, …, X n ) = β almost surely. The best bounds for β are still those originally established by Beardwood, Halton and Hammersley, namely 0.625 ≤ β ≤ 0.922. We slightly improve both upper and lower bounds.

Integrating Task and Motion Planning for Unmanned Aerial Vehicles

2014 ◽  
Vol 02 (01) ◽  
pp. 19-38 ◽  
Author(s):  
Matthew S. Cons ◽  
Tal Shima ◽  
Carmel Domshlak
Keyword(s):  
Motion Planning ◽  
Unmanned Aerial Vehicle ◽  
Traveling Salesman Problem ◽  
Upper Bound ◽  
Search Algorithm ◽  
Integrated Approach ◽  
Traveling Salesman ◽  
Aerial Vehicle ◽  
Path Cost ◽  
The Cost

This paper investigates the problem where a fixed-winged unmanned aerial vehicle is required to find the shortest flyable path to traverse over multiple targets. The unmanned aerial vehicle is modeled as a Dubins vehicle: a vehicle with a minimum turn radius and the inability to go backward. This problem is called the Dubins traveling salesman problem, an extension of the well-known traveling salesman problem. We propose and compare different algorithms that integrate the task planning and the motion planning aspects of the problem, rather than treating the two separately. An upper bound on calculating kinematic satisfying paths for setting costs in the search algorithm is investigated. The proposed integrated algorithms are compared to hierarchical algorithms that solve the search aspect first and then solve the motion planning aspect second. Monte Carlo simulations are performed for a range of vehicle turn radii. The simulations results show the viability of the integrated approach and that using two plausible kinematic satisfying paths as an upper bound to determine the cost-so-far into a search algorithm generally improves performance in terms of the shortest path cost and search complexity.

scholarly journals Asymmetric Traveling Salesman Path and Directed Latency Problems

2013 ◽  
Vol 42 (4) ◽  
pp. 1596-1619 ◽  
Author(s):  
Zachary Friggstad ◽  
Mohammad R. Salavatipour ◽  
Zoya Svitkina
Keyword(s):  
Traveling Salesman ◽  
Traveling Salesman Path
Sign in / Sign up

Export Citation Format

Share Document