Optimal Bitonic Tour

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Bitonic tour - GitHub Pages

http://marcodiiga.github.io/bitonic-tour

Oct 03, 2015 · It is defined as the optimal bitonic tour the minimum-length path which forms a bitonic tour. The best bitonic tour also minimizes the horizontal motion while covering all of the vertices in the set. Let us consider for instance the following set of points in …

Algorithm::TravelingSalesman::BitonicTour - solve the ...

https://metacpan.org/pod/Algorithm::TravelingSalesman::BitonicTour

Sep 29, 2008 · An open bitonic tour, optimal or not, has these properties: * it's bitonic (a vertical line crosses the tour at most twice) * it's open (it has endpoints), which we call "i" and "j" (i < j) * all points to the left of "j" are visited by the tour * points i and j are endpoints (connected to exactly one edge) * all other points in the tour are ...

algorithm - How to compute optimal paths for traveling ...

https://stackoverflow.com/questions/874982/how-to-compute-optimal-paths-for-traveling-salesman-bitonic-tour

you have a known property of the problems that let's you prove the solution is really optimal under some measure of optimality. (In this case, shortest.) The essential property of a bitonic tour is that a vertical line in the coordinate system crosses a side of the closed polygon at most twice. So, what is a bitonic tour of exactly two points?

Tutorial 3 - Lunds tekniska högskola

http://fileadmin.cs.lth.se/cs/Personal/Rolf_Karlsson/tut3.pdf

Optimal substructure again applies: the subpath from pk to pj−1 must be a shortest bitonic path Pk,j−1. The length of Pij is therefore given by min1≤k<j−1{b[k,j −1] +pkpj}. In an optimal bitonic tour, one of the points adjacent to pn must be pn−1, so b[n,n] = b[n − 1,n] …

Assignment 4 - cs.huji.ac.il

http://www.cs.huji.ac.il/course/2004/algo/Solutions/bitonic.pdf

Hence, the tour cannot be bitonic. Observation 1 implies that edge (p n−1,p n) is present in any bitonic tour that visits all points. Hence, to find a shortest such tour, it suffices to concentrate on minimizing the length of the bitonic path from p n−1 to p n that is obtained by removing edge (p n−1,p n) from the tour.

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