The Huffman Tree Problem with Upper-Bounded Linear Functions
Summary :
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.
- Publication
- IEICE TRANSACTIONS on Information Vol.E105-D No.3 pp.474-480
- Publication Date
- 2022/03/01
- Publicized
- 2021/10/12
- Online ISSN
- 1745-1361
- DOI
- 10.1587/transinf.2021FCP0006
- Type of Manuscript
- Special Section PAPER (Special Section on Foundations of Computer Science - New Trends of Theory of Computation and Algorithm -)
- Category
Authors
Hiroshi FUJIWARA
Shinshu University
Yuichi SHIRAI
Shinshu University
Hiroaki YAMAMOTO
Shinshu University
Keyword
Latest Issue
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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
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@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},}
Copy
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 -
English
