Bounding the Depth of Search Trees

@article{Fraenkel1993BoundingTD,
  title={Bounding the Depth of Search Trees},
  author={Aviezri S. Fraenkel and Shmuel Tomi Klein},
  journal={Comput. J.},
  year={1993},
  volume={36},
  pages={668-678}
}
For an ordered sequence of n weights, Human's algorithm constructs in time and space O(n) a search tree with minimum average path length, or, with is equivalent, a minimum redundancy code. However, if an upper bound B is imposed on the length of the codewords, the best known algorithms for the construction of an optimal code have time and space complexities O(Bn 2 ). A new algorithm is presented, which yields sub-optimal codes, but in time O(n log n) and space O(n). Under certain conditions… 
View via Publisher
academic.oup.com
33 Citations
Highly Influential Citations
3
Background Citations
8
Methods Citations
12
Results Citations
2

33 Citations

Incremental Calculation of Minimum-Redundancy Length-Restricted Codes
TLDR
This paper presents an algorithm which computes a minimum-redundancy length-restricted code in O((H L + 1)n) time, by starting with a Minimum Redundancy (Huffman) code with a maximum codeword length of H, and then refining it to meet the length limit L.
Efficient Construction of Minimum-Redundancy Codes for Large Alphabets
TLDR
Borders are shown that a minimum-redundancy prefix code can be constructed in O(r+r log(n/r) time, and a minimum redundancy L-bit length-limited prefix codeCan be constructed on a sorted-by-weight alphabet of n symbols and r distinct symbol weights.
Efficient Implementation of the WARM-UP Algorithm for the Construction of Length-Restricted Prefix Codes
TLDR
This paper proposes an efficient implementation of the WARM-UP algorithm, an approximative method for the length-restricted prefix code problem, and overcomes the LRR Package Method, the faster known exact method.
Practical Use of The Warm-up Algorithm onLength-Restricted
TLDR
The proposed implementation of the WARM-UP Algorithm has the same time complexity, but requires only additional O(1) space and some empirical experiments show that this algorithm provides good compression and speed performances.
In-place length-restricted prefix coding
  • R. Milidiú, A. Pessoa, E. Laber
  • Computer Science
    Proceedings. String Processing and Information Retrieval: A South American Symposium (Cat. No.98EX207)
  • 1998
TLDR
An in-place, simple and fast implementation for the BRCI (Build, Remove, Condense and Insert) algorithm, an approximative method for length-restricted coding, which overwrites a sorted input list of n weights with the corresponding codeword lengths in O(n) time.
Eecient Implementation of the Warm-up Algorithm for the Construction of Length-restricted Preex Codes
TLDR
This paper presents an eecient implementation of the WARM-UP algorithm, an approximative method for the length-restricted preex code problem, and overcomes the LRR Package Method, the faster known exact method.
Incremental calculation of minimum-redundancy length-restricted codes
TLDR
The package-merge strategy of Larmore and Hirschberg (1990) is a two-stage mechanism for creating minimum-redundancy length-restricted codes and the underlying strategy, here called ORIGINAL-PM, requires O(nL) time and space.
Space-efficient construction of optimal prefix codes
Shows that the use of the lazy list processing technique from the world of functional languages allows, under certain conditions, the package-merge algorithm to be executed in much less space than is…
Dynamic Length-Restricted Coding
TLDR
A new algorithm for constructing node-oriented alphabetic minimax trees and how to efficiently implement an abstract data type that stores a dynamic list of non-negative integers and supports an operation to determine whether there exists a binary tree on nodes of those depths.
Bounding the Inefficiency of Length-Restricted Prefix Codes
TLDR
The results presented in this paper suggest that one can efficiently implement length restricted prefix codes, obtaining also very effective codes.
...
...

References

SHOWING 1-10 OF 25 REFERENCES
Optimal Binary Search Trees with Restricted Maximal Depth
  • M. Garey
  • Computer Science
    SIAM J. Comput.
  • 1974
An algorithm is given for constructing a binary tree of minimum weighted path length for n nonnegative weights under the constraint that no path length exceed a given bound L. The number of…
Path Length of Binary Search Trees.
TLDR
It is shown that Huffman’s algorithm for optimal binary trees coincides with the T-C algorithms for optimal alphabetic binary trees when the terminal nodes have monotonically increasing weights from left to right.
Two inequalities implied by unique decipherability
TLDR
A consequence of (1) and work of Shannon is that this more restricted kind of list suffices in the search for codes with specified amounts of redundancy.
Novel Compression of Sparse Bit-Strings — Preliminary Report
TLDR
New methods for the compression of large sparse binary strings based on various new numeration systems in which the lengths of zero-block runs are represented, superior to previously known methods are presented.
A method for the construction of minimum-redundancy codes
  • D. Huffman
  • Computer Science, Business
    Proceedings of the IRE
  • 1952
TLDR
A minimum-redundancy code is one constructed in such a way that the average number of coding digits per message is minimized.
Variable-length binary encodings
This paper gives a theoretical treatment of several properties which describe certain variable-length binary encodings of the sort which could be used for the storage or transmission of information.…
The advanced theory of language as choice and chance
The art of computer programming: V.1.: Fundamental algorithms
Cryptanalysis: A Study of Ciphers and Their Solution
Information retrieval, computational and theoretical aspects
...
...