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Revisiting the Top-Down Computation of BDD of Spanning Trees of a Graph and Its Tutte Polynomial
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Summary :
Revisiting the Sekine-Imai-Tani top-down algorithm to compute the BDD of all spanning trees and the Tutte polynomial of a given graph, we explicitly analyze the Fixed-Parameter Tractable (FPT) time complexity with respect to its (proper) pathwidth, pw (ppw), and obtain a bound of O*(Bellmin{pw}+1,ppw}), where Belln denotes the n-th Bell number, defined as the number of partitions of a set of n elements. We further investigate the case of complete graphs in terms of Bell numbers and related combinatorics, obtaining a time complexity bound of Belln-O(n/log n).
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E102-A No.9 pp.1022-1027
- Publication Date
- 2019/09/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E102.A.1022
- Type of Manuscript
- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
- Category
- Graph algorithms
Authors
Farley Soares OLIVEIRA
The University of Tokyo
Hidefumi HIRAISHI
The University of Tokyo
Hiroshi IMAI
The University of Tokyo
Keyword
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Farley Soares OLIVEIRA, Hidefumi HIRAISHI, Hiroshi IMAI, "Revisiting the Top-Down Computation of BDD of Spanning Trees of a Graph and Its Tutte Polynomial" in IEICE TRANSACTIONS on Fundamentals,
vol. E102-A, no. 9, pp. 1022-1027, September 2019, doi: 10.1587/transfun.E102.A.1022.
Abstract: Revisiting the Sekine-Imai-Tani top-down algorithm to compute the BDD of all spanning trees and the Tutte polynomial of a given graph, we explicitly analyze the Fixed-Parameter Tractable (FPT) time complexity with respect to its (proper) pathwidth, pw (ppw), and obtain a bound of O*(Bellmin{pw}+1,ppw}), where Belln denotes the n-th Bell number, defined as the number of partitions of a set of n elements. We further investigate the case of complete graphs in terms of Bell numbers and related combinatorics, obtaining a time complexity bound of Belln-O(n/log n).
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.1022/_p
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@ARTICLE{e102-a_9_1022,
author={Farley Soares OLIVEIRA, Hidefumi HIRAISHI, Hiroshi IMAI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Revisiting the Top-Down Computation of BDD of Spanning Trees of a Graph and Its Tutte Polynomial},
year={2019},
volume={E102-A},
number={9},
pages={1022-1027},
abstract={Revisiting the Sekine-Imai-Tani top-down algorithm to compute the BDD of all spanning trees and the Tutte polynomial of a given graph, we explicitly analyze the Fixed-Parameter Tractable (FPT) time complexity with respect to its (proper) pathwidth, pw (ppw), and obtain a bound of O*(Bellmin{pw}+1,ppw}), where Belln denotes the n-th Bell number, defined as the number of partitions of a set of n elements. We further investigate the case of complete graphs in terms of Bell numbers and related combinatorics, obtaining a time complexity bound of Belln-O(n/log n).},
keywords={},
doi={10.1587/transfun.E102.A.1022},
ISSN={1745-1337},
month={September},}
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TY - JOUR
TI - Revisiting the Top-Down Computation of BDD of Spanning Trees of a Graph and Its Tutte Polynomial
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1022
EP - 1027
AU - Farley Soares OLIVEIRA
AU - Hidefumi HIRAISHI
AU - Hiroshi IMAI
PY - 2019
DO - 10.1587/transfun.E102.A.1022
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E102-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2019
AB - Revisiting the Sekine-Imai-Tani top-down algorithm to compute the BDD of all spanning trees and the Tutte polynomial of a given graph, we explicitly analyze the Fixed-Parameter Tractable (FPT) time complexity with respect to its (proper) pathwidth, pw (ppw), and obtain a bound of O*(Bellmin{pw}+1,ppw}), where Belln denotes the n-th Bell number, defined as the number of partitions of a set of n elements. We further investigate the case of complete graphs in terms of Bell numbers and related combinatorics, obtaining a time complexity bound of Belln-O(n/log n).
ER -
English
