The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
A construção de um código de Huffman pode ser entendida como o problema de encontrar uma árvore binária completa tal que cada folha esteja associada a uma função linear da profundidade da folha e a soma dos valores da função seja minimizada. Fujiwara e Jacobs estenderam isso para uma função geral e provaram que o problema estendido era NP-difícil. Os autores também mostraram o caso em que as funções associadas às folhas são não decrescentes e convexas podem ser resolvidas em tempo polinomial. No entanto, a complexidade do caso de funções não convexas não decrescentes permanece desconhecida. Neste artigo, tentamos revelar a complexidade considerando funções não decrescentes e não convexas, cada uma das quais assume o menor valor de uma função linear ou de uma constante. Como resultado, fornecemos um algoritmo de tempo polinomial para duas subclasses de tais funções.
Hiroshi FUJIWARA
Shinshu University
Yuichi SHIRAI
Shinshu University
Hiroaki YAMAMOTO
Shinshu University
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Copiar
Hiroshi FUJIWARA, Yuichi SHIRAI, Hiroaki YAMAMOTO, "The Huffman Tree Problem with Upper-Bounded Linear Functions" in IEICE TRANSACTIONS on Information,
vol. E105-D, no. 3, pp. 474-480, March 2022, doi: 10.1587/transinf.2021FCP0006.
Abstract: The construction of a Huffman code can be understood as the problem of finding a full binary tree such that each leaf is associated with a linear function of the depth of the leaf and the sum of the function values is minimized. Fujiwara and Jacobs extended this to a general function and proved the extended problem to be NP-hard. The authors also showed the case where the functions associated with leaves are each non-decreasing and convex is solvable in polynomial time. However, the complexity of the case of non-decreasing non-convex functions remains unknown. In this paper we try to reveal the complexity by considering non-decreasing non-convex functions each of which takes the smaller value of either a linear function or a constant. As a result, we provide a polynomial-time algorithm for two subclasses of such functions.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2021FCP0006/_p
Copiar
@ARTICLE{e105-d_3_474,
author={Hiroshi FUJIWARA, Yuichi SHIRAI, Hiroaki YAMAMOTO, },
journal={IEICE TRANSACTIONS on Information},
title={The Huffman Tree Problem with Upper-Bounded Linear Functions},
year={2022},
volume={E105-D},
number={3},
pages={474-480},
abstract={The construction of a Huffman code can be understood as the problem of finding a full binary tree such that each leaf is associated with a linear function of the depth of the leaf and the sum of the function values is minimized. Fujiwara and Jacobs extended this to a general function and proved the extended problem to be NP-hard. The authors also showed the case where the functions associated with leaves are each non-decreasing and convex is solvable in polynomial time. However, the complexity of the case of non-decreasing non-convex functions remains unknown. In this paper we try to reveal the complexity by considering non-decreasing non-convex functions each of which takes the smaller value of either a linear function or a constant. As a result, we provide a polynomial-time algorithm for two subclasses of such functions.},
keywords={},
doi={10.1587/transinf.2021FCP0006},
ISSN={1745-1361},
month={March},}
Copiar
TY - JOUR
TI - The Huffman Tree Problem with Upper-Bounded Linear Functions
T2 - IEICE TRANSACTIONS on Information
SP - 474
EP - 480
AU - Hiroshi FUJIWARA
AU - Yuichi SHIRAI
AU - Hiroaki YAMAMOTO
PY - 2022
DO - 10.1587/transinf.2021FCP0006
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E105-D
IS - 3
JA - IEICE TRANSACTIONS on Information
Y1 - March 2022
AB - The construction of a Huffman code can be understood as the problem of finding a full binary tree such that each leaf is associated with a linear function of the depth of the leaf and the sum of the function values is minimized. Fujiwara and Jacobs extended this to a general function and proved the extended problem to be NP-hard. The authors also showed the case where the functions associated with leaves are each non-decreasing and convex is solvable in polynomial time. However, the complexity of the case of non-decreasing non-convex functions remains unknown. In this paper we try to reveal the complexity by considering non-decreasing non-convex functions each of which takes the smaller value of either a linear function or a constant. As a result, we provide a polynomial-time algorithm for two subclasses of such functions.
ER -