The convex-hull-and-line traveling salesman problem: a solvable case

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Vladimir G. Deineko, René van Dal, Günter Rote
Information Processing Letters 51(3), pages 141–148
August 1994

We solve the special case of the Euclidean Traveling Salesman Problem where n − m cities lie on the boundary of the convex hull of all n cities, and the other m cities lie on a line segment inside this convex hull by an algorithm which needs O(mn) time and Othumb_down space.

keywords   Euclidean Traveling Salesman Problem, Shortest path, Well-solvable case, Polynomial time algorithm
journal or series
book Information Processing Letters (IPL)