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
Pembinaan kod Huffman boleh difahami sebagai masalah mencari pokok binari penuh supaya setiap daun dikaitkan dengan fungsi linear kedalaman daun dan jumlah nilai fungsi diminimumkan. Fujiwara dan Jacobs memanjangkan ini kepada fungsi umum dan membuktikan masalah lanjutan adalah NP-hard. Penulis juga menunjukkan kes di mana fungsi yang berkaitan dengan daun adalah setiap satu tidak berkurangan dan cembung boleh diselesaikan dalam masa polinomial. Walau bagaimanapun, kerumitan kes fungsi bukan cembung tidak berkurangan masih tidak diketahui. Dalam makalah ini kami cuba mendedahkan kerumitan dengan mempertimbangkan fungsi bukan cembung tidak menurun yang setiap satunya mengambil nilai yang lebih kecil sama ada fungsi linear atau pemalar. Akibatnya, kami menyediakan algoritma masa polinomial untuk dua subkelas fungsi tersebut.
Hiroshi FUJIWARA
Shinshu University
Yuichi SHIRAI
Shinshu University
Hiroaki YAMAMOTO
Shinshu University
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Salinan
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
Salinan
@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},}
Salinan
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 -