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Euclidean TSP (part I)
, 1996
"... Marios Papaefthymiou and Mike Klugerman. 1 Euclidean TSP Consider the travelling salesman problem in the plane. Given n points in the plane, we would like to nd a tour that visits all of them and that minimizes the distance travelled, where the distance between two points is given by the Euclidean ..."
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Marios Papaefthymiou and Mike Klugerman. 1 Euclidean TSP Consider the travelling salesman problem in the plane. Given n points in the plane, we would like to nd a tour that visits all of them and that minimizes the distance travelled, where the distance between two points is given by the Euclidean
Euclidean TSP on Two Polygons
, 2005
"... We give an O(n² m+nm² +m² log m) time and O(n² +m²) space algorithm for finding the shortest traveling salesman tour through the vertices of two simple polygonal obstacles in the Euclidean plane, where n and m are the number of vertices of the two polygons. The Euclidean TSP (ETSP) is the problem of ..."
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We give an O(n² m+nm² +m² log m) time and O(n² +m²) space algorithm for finding the shortest traveling salesman tour through the vertices of two simple polygonal obstacles in the Euclidean plane, where n and m are the number of vertices of the two polygons. The Euclidean TSP (ETSP) is the problem
6.1 Euclidean TSP
"... Today we continue the discussion of a dynamic programming (DP) approach to the Euclidean Travelling Salesman Problem (TSP). Finally, a randomized modification in introduced which acheives an expected approximation factor of 1 + 2ǫ. ..."
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Today we continue the discussion of a dynamic programming (DP) approach to the Euclidean Travelling Salesman Problem (TSP). Finally, a randomized modification in introduced which acheives an expected approximation factor of 1 + 2ǫ.
Polynomial time approximation schemes for Euclidean TSP and other geometric problems
 In Proceedings of the 37th IEEE Symposium on Foundations of Computer Science (FOCS’96
, 1996
"... Abstract. We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c � 1 and given any n nodes in � 2, a randomized version of the scheme finds a (1 � 1/c)approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. When the nodes a ..."
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Cited by 399 (3 self)
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Abstract. We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c � 1 and given any n nodes in � 2, a randomized version of the scheme finds a (1 � 1/c)approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. When the nodes
ffl)Approximation Scheme for the Euclidean TSP
, 1996
"... if the bounding box was the smallest possible, the length OPT of the optimum tour is at least 2n 2 (since there must be cities on the 2 shortest sides). Now, consider the instance obtained by rounding the coordinates of every city to the nearest integer. In the rounded instance, the distance betwe ..."
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if the bounding box was the smallest possible, the length OPT of the optimum tour is at least 2n 2 (since there must be cities on the 2 shortest sides). Now, consider the instance obtained by rounding the coordinates of every city to the nearest integer. In the rounded instance, the distance between any two distinct cities is at least 1. Moreover, in the transformation, every city has moved by at most p 2=2. For any tour T , let l(T ) and l 0 (T ) denote its length in the original and transformed instances respectively. Since we can perform an excursion from the new location to the old location of any city (or vice versa), we derive that jl(T ) \Gamma l 0 (T )j p 2n: (1) Thus, if we have a (1 + ffl<
A linear time approximation scheme for Euclidean TSP
"... Abstract—The Traveling Salesman Problem (TSP) is among the most famous NPhard optimization problems. The special case of TSP in boundeddimensional Euclidean spaces has been a particular focus of research: The celebrated results of Arora [Aro98] and Mitchell [Mit99] – along with subsequent improve ..."
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Cited by 1 (1 self)
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Abstract—The Traveling Salesman Problem (TSP) is among the most famous NPhard optimization problems. The special case of TSP in boundeddimensional Euclidean spaces has been a particular focus of research: The celebrated results of Arora [Aro98] and Mitchell [Mit99] – along with subsequent
On approximately fair cost allocation in Euclidean TSP games
, 1996
"... We consider the problem of allocating the cost of an optimal traveling salesman tour in a fair way among the nodes visited; in particular, we focus on the case where the distance matrix of the underlying TSP problem satisfies the triangle inequality. We thereby use the model of TSP games in the sens ..."
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Cited by 12 (3 self)
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We consider the problem of allocating the cost of an optimal traveling salesman tour in a fair way among the nodes visited; in particular, we focus on the case where the distance matrix of the underlying TSP problem satisfies the triangle inequality. We thereby use the model of TSP games
The Natural Crossover for the 2D Euclidean TSP
"... For the traveling salesman problem various search algorithms have been suggested for decades. In the field of genetic algorithms, many genetic operators have been introduced for the problem. Most genetic encoding schemes have some restrictions that cause moreorless loss of information contained in ..."
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Cited by 7 (4 self)
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in problem instances. We suggest a new encoding/crossover pair which pursues minimal information loss in chromosomal encoding and minimal restriction in recombination for the 2D Euclidean traveling salesman problem. The most notable feature of the suggested crossover is that it is based on a totally new
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