Optimal Bitonic Tour Algorithm

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

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

Clarification on your algorithm. The l(i,j) recursive function should compute the minimum distance of a bitonic tour i -> 1 -> j visiting all nodes that are smaller than i. ... -> j tour which is optimal. However traversing this route backward will give us the same distance, and won't broke bitonic property. Now the easy cases (note the changes

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 connected to two edges

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 …

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.

Introduction to Algorithms, Third Edition

https://www.csie.ntu.edu.tw/~hsinmu/courses/_media/dsa2_11spring/p403-405_p425-427.pdf

Describe an O.n2/-time algorithm for determining an optimal bitonic tour. You may assume that no two points have the samex-coordinate and that all operations on real numbers take unit time. (Hint:Scan left to right, maintaining optimal pos- sibilities for the two parts of the tour.) 15-4 Printing neatly

15.5 Optimal binary search trees

http://www.euroinformatica.ro/documentation/programming/!!!Algorithms_CORMEN!!!/DDU0091.html

Figure 15.9(b) shows the shortest bitonic tour of the same 7 points. In this case, a polynomial-time algorithm is possible. Describe an O(n 2)-time algorithm for determining an optimal bitonic tour. You may assume that no two points have the same x-coordinate.

Tutorial 3 - Lunds tekniska högskola

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

In an optimal bitonic tour, one of the points adjacent to pn must be pn−1, so b[n,n] = b[n − 1,n] + pn−1pn. To reconstruct the points on the shortest bitonic tour, we define r[i,j] to be the index of the immediate predecessor of pj on the shortest bitonic path Pij. Because the immediate predecessor of p2

Design and Analysis of Algorithms, Fall 2014 II-1

https://www.cs.helsinki.fi/webfm_send/1449

one of the paths. We describe a dynamic programming algorithm which uses partially constructed bitonic tours. For i; j 2f1;:::;ngand i, j on separate paths, let B[i; j] be the minimum total cost of two paths. Now the length of the optimal bitonic tour is given by B[n;n]. Since B[i; j] = B[j;i], we are only interested in pairs i; j with 1 i j n.

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