scholarly journals The Asymmetric Traveling Salesman Path LP Has Constant Integrality Ratio

2019 ◽  
pp. 288-298 ◽  
Author(s):  
Anna Köhne ◽  
Vera Traub ◽  
Jens Vygen
Keyword(s):  
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.

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

scholarly journals New Bounds for the Traveling Salesman Constant

2015 ◽  
Vol 47 (1) ◽  
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 X1, X2, …, Xn be independent and uniformly distributed random variables in the unit square [0, 1]2, and let L(X1, …, Xn) 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 limn→∞n−1/2L(X1, …, Xn) = 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.

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