Height restricted optimal binary trees
SIAM Journal on Computing
The concave least-weight subsequence problem revisited
Journal of Algorithms
A fast algorithm for optimal length-limited Huffman codes
Journal of the ACM (JACM)
Parallel construction of trees with optimal weighted path length
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
Constructing Huffman Trees in Parallel
SIAM Journal on Computing
Perspectives of Monge properties in optimization
Discrete Applied Mathematics
Placing resources on a growing line
Journal of Algorithms
Computing a minimum weight k-link path in graphs with the concave Monge property
Journal of Algorithms - Special issue on SODA '95 papers
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
A linear space algorithm for computing maximal common subsequences
Communications of the ACM
Optimal sequential paging in cellular wireless networks
Wireless Networks
Online dynamic programming speedups
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Asymptotic average redundancy of Huffman (and other) block codes
IEEE Transactions on Information Theory
Monge strikes again: optimal placement of web proxies in the internet
Operations Research Letters
Hi-index | 754.84 |
The "state-of-the-art" in length-limited Huffman coding (LLHC) algorithms is the Θ(nD)-time, Θ(n)-space one of Hirschberg and Larmore, where n is the size of the code and D ≤ n is the length restriction on the codewords. This is a very clever, very problem specific, technique. This paper presents a simple dynamic-programming (DP) method that solves the problem with the same time and space bounds. The fact that there was an Θ(nD) time DP algorithm was previously known; it is a straightforward DP with the Monge property (which permits an order of magnitude speedup). It was not interesting, though, because it also required Θ(nD) space. The main result of this paper is the technique developed for reducing the space. It is quite simple and applicable to many other problems modeled by DPs with the Monge property. This is illustrated with examples from web-proxy design and wireless mobile paging.