On the Spacefilling Curve Heuristic for the Eculidean Traveling Salesman Problem
On the Spacefilling Curve Heuristic for the Eculidean Traveling Salesman Problem
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In our eReader you can find the full English version of the book. Read On the Spacefilling Curve Heuristic for the Eculidean Traveling Salesman Problem Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book On the Spacefilling Curve Heuristic for the Eculidean Traveling Salesman Problem
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Hence a A b k _ 2 +a fc _i/2 + J12 +J23 = (afc_2 + a*-i)/2 + . 7i2 + j 2A where j 12 is the length of the jump from the last point in T] to the first point in T 2 . And j 2 3 is the length of the jump from the last point in T 2 to the first point in T 3 . To estimate these jump lengths we need to know the first and last points of S'n visited in each subtriangle.
Lemma 2. 2 For n = 2 k, k > 1, the first point in S n (and by similarity S' n ) under order is (xi, yi), and the last point is ( ...x p, y p ) where p = (n/2) + 1.
Figure 2: The set 5i 6 in the unit triangle T decomposes into a copy of S' 4 in 7\, a reversed copy of S' 4 in T 2, and a reversed copy of Sg in T 3 . Curve visits the leftmost point first and the ninth point last (marked by arrowheads).
Proof: Let the points of S n be indexed as in the definition (1). By inspection for k 3, we again use figure 2. The first point of S n in T is the first point in T\. The points in S n f] Ji are {(z t, ?/, ), 1
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To quickly assess the difficulty of the text, read a short excerpt:
Hence a A b k _ 2 +a fc _i/2 + J12 +J23 = (afc_2 + a*-i)/2 + . 7i2 + j 2A where j 12 is the length of the jump from the last point in T] to the first point in T 2 . And j 2 3 is the length of the jump from the last point in T 2 to the first point in T 3 . To estimate these jump lengths we need to know the first and last points of S'n visited in each subtriangle.
Lemma 2. 2 For n = 2 k, k > 1, the first point in S n (and by similarity S' n ) under order
Figure 2: The set 5i 6 in the unit triangle T decomposes into a copy of S' 4 in 7\, a reversed copy of S' 4 in T 2, and a reversed copy of Sg in T 3 . Curve
Proof: Let the points of S n be indexed as in the definition (1). By inspection for k 3, we again use figure 2. The first point of S n in T is the first point in T\. The points in S n f] Ji are {(z t, ?/, ), 1
What to read after On the Spacefilling Curve Heuristic for the Eculidean Traveling Salesman Problem?
You can find similar books in the "Read Also" column, or choose other free books by Dimitris Bertsimas to read online
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