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On the Spacefilling Curve Heuristic for the Euclidean Traveling Salesman Problem
Excerpt from On the Spacefilling Curve Heuristic for the Euclidean Traveling Salesman Problem
Now we describe the heuristic of given a set S of n points in the unit square, visit the points in the order qs defined above, and finish the tour by returning to the first point. As remarked in this heuristic is very fast. Given point (x, y) input as a pair of k-bit fractions, a 2k-bit sorting key t may be computed in O(k) bit operations (t is really an inverse y) where (15 is defined as a continuous map from the unit interval onto the unit square). Given n such points, all the keys may be computed and then sorted (by radix-sort [l]) in O(kn) bit operations, i.e. In time linear in the input size.
Now we describe the heuristic of given a set S of n points in the unit square, visit the points in the order qs defined above, and finish the tour by returning to the first point. As remarked in this heuristic is very fast. Given point (x, y) input as a pair of k-bit fractions, a 2k-bit sorting key t may be computed in O(k) bit operations (t is really an inverse y) where (15 is defined as a continuous map from the unit interval onto the unit square). Given n such points, all the keys may be computed and then sorted (by radix-sort [l]) in O(kn) bit operations, i.e. In time linear in the input size.
14 pages, Paperback
Published August 24, 2018
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