Building bridges between convex regions

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Abstract

In the Euclidean traveling salesman and buyers problem (TSBP), we are given a set of convex regions in d-dimensional space, and we wish to find a minimum-cost tour that visits all the regions. The cost of a tour depends on the length of the tour itself and on the distance that buyers within each region need to travel to meet the salesman. We show that constant-factor approximations to the TSBP and several similar problems can be obtained by visiting the centers of the smallest enclosing spheres of the regions. © 2002 Elsevier Science B.V.

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Ahn, H. K., Cheong, O., & Shin, C. S. (2003). Building bridges between convex regions. Computational Geometry: Theory and Applications, 25(1–2), 161–170. https://doi.org/10.1016/S0925-7721(02)00135-9

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