scholarly journals Efficient PTAS for the maximum traveling salesman problem in a metric space of fixed doubling dimension

2021 ◽  
Author(s):  
Vladimir Shenmaier
Keyword(s):  
Traveling Salesman Problem ◽  
Metric Space ◽  
Traveling Salesman ◽  
Doubling Dimension ◽  
Maximum Traveling Salesman Problem

THE MAXIMUM TRAVELING SALESMAN PROBLEM ON BANDED MATRICES

2001 ◽  
Vol 12 (06) ◽  
pp. 809-819 ◽  
Author(s):  
DAVID BLOKH ◽  
EUGENE LEVNER
Keyword(s):  
Traveling Salesman Problem ◽  
Linear Time ◽  
Time Algorithm ◽  
Traveling Salesman ◽  
Problem Size ◽  
Principal Diagonal ◽  
Banded Matrix ◽  
Banded Matrices ◽  
Maximum Traveling Salesman Problem ◽  
Distance Matrices

We investigate the Maximum Traveling Salesman Problem on banded distance matrices. A (p, q)-banded matrix has all its non-zero elements contained within a band consisting of p diagonals above the principal diagonal and q diagonals below it. We investigate the properties of the problem and prove that the number K of different permutations which can be optimal solutions for different instances of the problem, is exponential in n where n is the problem size (= the number of cities). For the Maximum-TSP on the (2, 0)-banded matrices, K=O(λn) where 1.7548 <λ< 1.7549, whereas on the (1, 1)-banded matrices K=O(λn) where 1.6180 <λ< 1.6181. Using recursive equations, we derive a linear-time algorithm that exactly solves the Maximum-TSP on the (2, 0)-banded distance matrices.

scholarly journals The geometric maximum traveling salesman problem

2003 ◽  
Vol 50 (5) ◽  
pp. 641-664 ◽  
Author(s):  
Alexander Barvinok ◽  
Sándor P. Fekete ◽  
David S. Johnson ◽  
Arie Tamir ◽  
Gerhard J. Woeginger ◽  
...  
Keyword(s):  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Maximum Traveling Salesman Problem
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