A generalization of the convex-hull-and-line traveling salesman problem
1998 ◽
Vol 2
(2)
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pp. 177-191
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Keyword(s):
Two instances of the traveling salesman problem, on the same node set {1,2,…,n} but with different cost matrices C and C′ , are equivalent iff there exist {ai,bi: i=1,…, n} such that for any 1≤i, j≤n,i≠j,C′(i,j)=C(i,j)+ai+bj [7]. One of the well-solved special cases of the traveling salesman problem (TSP) is the convex-hull-and-line TSP. We extend the solution scheme for this class of TSP given in [9] to a more general class which is closed with respect to the above equivalence relation. The cost matrix in our general class is a certain composition of Kalmanson matrices. This gives a new, non-trivial solvable case of TSP.
1994 ◽
Vol 60
(2-3)
◽
pp. 171-177
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1994 ◽
Vol 51
(3)
◽
pp. 141-148
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