Optimal Leaf Ordering of Complete Binary Trees
Optimal Leaf Ordering of Complete Binary Trees
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2007
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Journal of Discrete Algorithms ; 5 (2007), 3. - pp. 546-552
Abstract
Ordering a set of items so as to minimize the sum of distances between consecutive elements is a fundamental optimization problem occurring in many settings. While it is View the MathML source-hard in general, it becomes polynomially solvable if the set of feasible permutations is restricted to be compatible with a tree of bounded degree. We present a new algorithm for the elementary case of ordering the n leaves of a binary tree with height View the MathML source. Our algorithm requires View the MathML source time and View the MathML source space. While the running time is a log-factor away from being asymptotically optimal, the algorithm is conceptually simple, easy to implement, and highly practical. Its implementation requires little more than a few bit-manipulations.
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004 Computer Science
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optimal leaf ordering,bit-manipulation algorithms,permutations
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BRANDES, Ulrik, 2007. Optimal Leaf Ordering of Complete Binary Trees. In: Journal of Discrete Algorithms. 5(3), pp. 546-552. Available under: doi: 10.1016/j.jda.2006.09.003BibTex
@article{Brandes2007Optim-3022, year={2007}, doi={10.1016/j.jda.2006.09.003}, title={Optimal Leaf Ordering of Complete Binary Trees}, number={3}, volume={5}, journal={Journal of Discrete Algorithms}, pages={546--552}, author={Brandes, Ulrik} }
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