Optimal Leaf Ordering of Complete Binary Trees

Brandes, Ulrik

Optimal Leaf Ordering of Complete Binary Trees

Files

Brandes_opus-117791.pdf(149.43 KB)

Date

2007

Publication type

Journal article

Published in

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.

Subject (DDC)

004 Computer Science

Keywords

optimal leaf ordering,bit-manipulation algorithms,permutations

Cite This

ISO 690

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.2006.09.003

BibTex

@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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Bibliography of Konstanz

Yes