V. G. Deineko, R. van Dal, and G. Rote #1994# The convex-hull-and-line traveling salesman problem: A solvable case, Information Processing Letters 51, 141#148. Home/Search Document Details and Download
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The N-line Traveling Salesman Problem - Rote (1991) Self-citation (Rote) (Correct)
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V. G. Deineko, R. van Dal, and G. Rote #1994# The convex-hull-and-line traveling salesman problem: A solvable case, Information Processing Letters 51, 141#148.
The N-line Traveling Salesman Problem - Rote (1991) Self-citation (Rote) (Correct)
....algorithm was given in Gilmore, Lawler, and Shmoys [1985] section 15, for the Traveling Salesman Problem with limited bandwidth. That algorithm also has linear running time (for fixed bandwidth) Cutler s N line Traveling Salesman Problem has recently been generalized in a different direction by Deineko, van Dal, and Rote [1994]. They considered the problem where the given points lie on the boundary of a convex polygon and on one additional line segment inside this polygon. Clearly, this class of problems contains the 3 line Traveling Salesman Problem as a special case. Moreover, they improved the complexity from O(n 3 ....
V. G. Deineko, R. van Dal, and G. Rote [1994] The convex-hull-and-line traveling salesman problem: A solvable case, Information Processing Letters 51, 141--148.
Well-Solvable Special Cases of the TSP: A Survey - Burkard, Deineko, van Dal.. (1995) (2 citations) Self-citation (Deineko) (Correct)
.... C C a a a a i i i i H H H H Forbidden configurations Allowed configurations j j j ae ae Gamma Gamma Gamma Gamma Gamma Gamma Gamma Gamma ae ae ae ae ae ae X X X X X Gamma Gamma l l l Figure 2: Illustrations to the N line TSP In 1994, Deineko, Van Dal and Rote [37] investigated another related special case, the convexhull and line TSP. Here n Gamma m cities lie on the boundary of the convex hull of the n cities, and the remaining m cities lie on a line segment inside of this convex hull (see the left part of Figure 3) Clearly, this is another extension ....
.... lie on a line segment inside of this convex hull (see the left part of Figure 3) Clearly, this is another extension of Cutler s special case (in case the upper chain and the lower chain of the convex hull both degenerate to straight lines, one arrives at the 3 line TSP) Deineko, Van Dal and Rote [37] give an O(nm) O(n 2 ) time and O(n) space algorithm and thus obtain an improvement in both running time and space requirements over Cutler s algorithm. The algorithm computes a shortest path in a related edge weighted directed network. The edge weights in this network arise from Euclidean ....
V. Deineko, R. Van Dal and G. Rote, The convex-hull-and-line traveling salesman problem: a solvable case, Information Processing Letters 51, 1994, 141--148.
Long-Chord-Free and Fence-Free Tours for the Travelling.. - Deineko, Woeginger (1995) Self-citation (Deineko) (Correct)
....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] investigated another special case, the convex hull and line TSP: Here n Gamma m cities lie on the Lcf Free Tours for the TSP 3 Q Q Q ( Q Q B B B B B B B B , a a a a H H H H H H H H H H v v v v v v v v v v v v v v Q Q Q ( a a a a v v v v ....
V. Deineko, R. Van Dal and G. Rote, The convex-hull-and-line traveling salesman problem: a solvable case, Information Processing Letters 51, 1994, 141--148.
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