By Jurek Czyzowicz, David Ilcinkas, Arnaud Labourel (auth.), Haim Kaplan (eds.)
This ebook constitutes the court cases of the twelfth foreign Scandinavian Workshop on set of rules idea, held in Bergen, Norway in June 2010.
Read or Download Algorithm Theory - SWAT 2010: 12th Scandinavian Symposium and Workshops on Algorithm Theory, Bergen, Norway, June 21-23, 2010. Proceedings PDF
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Extra resources for Algorithm Theory - SWAT 2010: 12th Scandinavian Symposium and Workshops on Algorithm Theory, Bergen, Norway, June 21-23, 2010. Proceedings
When inserting a new element, a node is created. The new element and those associated with the root and its -child are compared; the two smallest among the three are associated with the root and its -child, and the largest is associated with the created node. Hereafter, the new node is added as a -child of rank 0 to the -child of the root. Since the cardinality sequence of that node was regular before the insertion, only O(1) structural changes are necessary to restore the regularity constraint.
That is, insert has O(1) worst-case cost. To meld two trees, the elements associated with the root and its -child are taken from both trees and these four elements are sorted. The largest element is 34 A. Elmasry, C. Jensen, and J. Katajainen associated with a -child of the root of one tree. Let T be that tree, and let S be the other tree. The two smallest elements are then associated with the root of S and its -child. Accordingly, the other two elements are associated with the root of T and its -child.
For the strictly-regular system, the exponentiality property holds by setting θ = c = Φ, where Φ is the golden ratio. Proof. Consider a sequence of digits in a strictly-regular representation, and think about di = 2 as two 1’s at position i. It is straightforward to verify that there exists a distinct 1 whose position is at least i, for every i from 0 to r − 2. r−1 r−2 In other words, we have i=0 di · si ≥ i=0 si . Substituting with si ≥ Φi−1 and r−1 r−3 i s0 = 1, we obtain i=0 di · si ≥ 1 + i=0 Φ ≥ Φr−1 − 1.
Algorithm Theory - SWAT 2010: 12th Scandinavian Symposium and Workshops on Algorithm Theory, Bergen, Norway, June 21-23, 2010. Proceedings by Jurek Czyzowicz, David Ilcinkas, Arnaud Labourel (auth.), Haim Kaplan (eds.)