Rote, G. #1992#, The N-line traveling salesman problem, Networks 22, 91#108.  Home/Search Document Not in Database Summary Related Articles Check |
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Well-Solvable Special Cases of the TSP: A Survey - Burkard, Deineko, van Dal.. (1995) (2 citations) (Correct)
....lie on parallel lines. It is easily seen that minimizing the total distance covered by the laser is equivalent to solving a TSP (cf. Lin and Kernighan [73] Cutler [28] developed an O(n 3 ) time and O(n 2 ) space dynamic programming algorithm for the case with k = 3 parallel lines. Rote [103] generalized Cutler s result and derived an O(n k ) algorithm for an arbitrary but fixed number of k 4 lines. This algorithm strongly builds on Flood s result that the shortest tour does not intersect itself. Moreover, Rote observed that the lines need not be exactly parallel but might be ....
....does not contain fences as subsets and it is called long chord free, if it does not contain long chords. Observe that long chord freeness and fence freeness are monotone properties of sets of edges and carries over to subsets. A dynamic programming approach quite similar to that one used by Rote [103] yields the following result. 3 SOLVABLE CASES OF THE EUCLIDEAN TSP 18 Q Q Q ( Q Q B B B B B B , a a a H H H H H H H H H t t t t t t t t t t t t t t Convex hull and line TSP Q Q Q ( a a a t t t t t t t t t a a a a t Convex hull and k line ....
G. Rote, The N -line traveling salesman problem, Networks 22, 1992, 91--108.
Long-Chord-Free and Fence-Free Tours for the Travelling.. - Deineko, Woeginger (1995) (Correct)
....holes in certain places of the board which usually lie on parallel lines. It is easily seen that minimizing the total distance covered by the laser is equivalent to solving a TSP (cf. Lin and Kernighan [7] Cutler [1] developed an O(n 3 ) algorithm for the case with k = 3 parallel lines. Rote [9] generalized Cutler s result and derived an O(n k ) algorithm for any fixed number of k 4 lines. Rote also observed that the lines need not be exactly parallel but might be slightly perturbated and slightly rotated without destroying polynomial solvability. Deineko, Van Dal and Rote [2] ....
....is a monotone property of sets of edges and carries over to subsets. 3 A Fast Algorithm In this section we design a fast dynamic programming algorithm for computing the shortest Lcf free tour for a given set P of cities. The algorithm extends (and in some sense simplifies) the ideas of Rote [9]. We start with some more definitions. Let L = 1 ; k ) be a k tuple of nonnegative integers with 0 i n i for 1 i k. By P (L) we denote the subset of P that consists of the i smallest cities of every class P i (with respect to the order OE) Moreover, for i 1 we denote by ....
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G. Rote, The N -line traveling salesman problem, Networks 22, 1992, 91-108.
The Convex-Hull-and-Line Traveling Salesman Problem: A.. - Deineko, Dal, Rote (1992) Self-citation (Rote) (Correct)
....to the case where all cities lie on the boundary of their convex hull. Cutler #1980# has given an O#n 3 # time and O#n 2 # space dynamic programming algorithm for solving the so called 3 line TSP, i.e. the Euclidean TSP where all points lie on three distinct parallel lines in the plane. Rote #1992# extended the results of Cutler by considering the N line TSP, i.e. the Euclidean TSP where all points lie on N parallel lines in the plane, with N a small integer. He gave a dynamic programming algorithm which is polynomial for a #xed number of lines. Moreover, conditions are given such that ....
Rote, G. #1992#, The N-line traveling salesman problem, Networks 22, 91#108.
The N-line Traveling Salesman Problem - Rote (1991) Self-citation (Rote) (Correct)
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The N-line Traveling Salesman Problem --- page 20 G. Rote #1988# The N-line Traveling Salesman Problem, Bericht 1988-109, Technische Universit#at Graz, Institut f#ur Mathematik, January 1988.
The Convex-Hull-and-Line Traveling Salesman Problem: A.. - Deineko, van Dal, Rote (1992) Self-citation (Rote) (Correct)
....to the case where all cities lie on the boundary of their convex hull. Cutler [1980] has given an O(n 3 ) time and O(n 2 ) space dynamic programming algorithm for solving the so called 3 line TSP, i.e. the Euclidean TSP where all points lie on three distinct parallel lines in the plane. Rote [1992] extended the results of Cutler by considering the N line TSP, i.e. the Euclidean TSP where all points lie on N parallel lines in the plane, with N a small integer. He gave a dynamic programming algorithm which is polynomial for a fixed number of lines. Moreover, conditions are given such that ....
Rote, G. (1992), The N-line traveling salesman problem, Networks 22, 91--108.
The N-line Traveling Salesman Problem - Rote (1991) (Correct)
No context found.
The N-line Traveling Salesman Problem --- page 20 G. Rote [1988] The N-line Traveling Salesman Problem, Bericht 1988-109, Technische Universitat Graz, Institut fur Mathematik, January 1988.
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