IEICE TRANSACTIONS on Information
Improvement of Steiner Tree Algorithm: Branch-Based Multi-Cast
Summary :
There is a well known Steiner tree algorithm called minimum-cost paths heuristic (MPH), which is used for many multicast network operations and is considered a benchmark for other Steiner tree algorithms. MPH's average case time complexity is O(m(l+nlog n)), where m is the number of end nodes, n is the number of nodes, and l is the number of links in the network, because MPH has to run Dijkstra's algorithm as many times as the number of end nodes. The author recently proposed a Steiner tree algorithm called branch-based multi-cast (BBMC), which produces exactly the same multicast tree as MPH in a constant processing time irrespective of the number of multicast end nodes. However, the theoretical result for the average case time complexity of BBMC was expressed as O(log m(l+nlog n)) and could not accurately reflect the above experimental result. This paper proves that the average case time complexity of BBMC can be shortened to O(l+nlog n), which is independent of the number of end nodes, when there is an upper limit of the node degree, which is the number of links connected to a node. In addition, a new parameter β is applied to BBMC, so that the multicast tree created by BBMC has less links on it. Even though the tree costs increase due to this parameter, the tree cost increase rates are much smaller than the link decrease rates.
- Publication
- IEICE TRANSACTIONS on Information Vol.E96-D No.12 pp.2743-2752
- Publication Date
- 2013/12/01
- Publicized
- Online ISSN
- 1745-1361
- DOI
- 10.1587/transinf.E96.D.2743
- Type of Manuscript
- PAPER
- Category
- Fundamentals of Information Systems
Authors
Hiroshi MATSUURA
NTT Corporation
Keyword
Latest Issue
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Hiroshi MATSUURA, "Improvement of Steiner Tree Algorithm: Branch-Based Multi-Cast" in IEICE TRANSACTIONS on Information,
vol. E96-D, no. 12, pp. 2743-2752, December 2013, doi: 10.1587/transinf.E96.D.2743.
Abstract: There is a well known Steiner tree algorithm called minimum-cost paths heuristic (MPH), which is used for many multicast network operations and is considered a benchmark for other Steiner tree algorithms. MPH's average case time complexity is O(m(l+nlog n)), where m is the number of end nodes, n is the number of nodes, and l is the number of links in the network, because MPH has to run Dijkstra's algorithm as many times as the number of end nodes. The author recently proposed a Steiner tree algorithm called branch-based multi-cast (BBMC), which produces exactly the same multicast tree as MPH in a constant processing time irrespective of the number of multicast end nodes. However, the theoretical result for the average case time complexity of BBMC was expressed as O(log m(l+nlog n)) and could not accurately reflect the above experimental result. This paper proves that the average case time complexity of BBMC can be shortened to O(l+nlog n), which is independent of the number of end nodes, when there is an upper limit of the node degree, which is the number of links connected to a node. In addition, a new parameter β is applied to BBMC, so that the multicast tree created by BBMC has less links on it. Even though the tree costs increase due to this parameter, the tree cost increase rates are much smaller than the link decrease rates.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.E96.D.2743/_p
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@ARTICLE{e96-d_12_2743,
author={Hiroshi MATSUURA, },
journal={IEICE TRANSACTIONS on Information},
title={Improvement of Steiner Tree Algorithm: Branch-Based Multi-Cast},
year={2013},
volume={E96-D},
number={12},
pages={2743-2752},
abstract={There is a well known Steiner tree algorithm called minimum-cost paths heuristic (MPH), which is used for many multicast network operations and is considered a benchmark for other Steiner tree algorithms. MPH's average case time complexity is O(m(l+nlog n)), where m is the number of end nodes, n is the number of nodes, and l is the number of links in the network, because MPH has to run Dijkstra's algorithm as many times as the number of end nodes. The author recently proposed a Steiner tree algorithm called branch-based multi-cast (BBMC), which produces exactly the same multicast tree as MPH in a constant processing time irrespective of the number of multicast end nodes. However, the theoretical result for the average case time complexity of BBMC was expressed as O(log m(l+nlog n)) and could not accurately reflect the above experimental result. This paper proves that the average case time complexity of BBMC can be shortened to O(l+nlog n), which is independent of the number of end nodes, when there is an upper limit of the node degree, which is the number of links connected to a node. In addition, a new parameter β is applied to BBMC, so that the multicast tree created by BBMC has less links on it. Even though the tree costs increase due to this parameter, the tree cost increase rates are much smaller than the link decrease rates.},
keywords={},
doi={10.1587/transinf.E96.D.2743},
ISSN={1745-1361},
month={December},}
Copy
TY - JOUR
TI - Improvement of Steiner Tree Algorithm: Branch-Based Multi-Cast
T2 - IEICE TRANSACTIONS on Information
SP - 2743
EP - 2752
AU - Hiroshi MATSUURA
PY - 2013
DO - 10.1587/transinf.E96.D.2743
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E96-D
IS - 12
JA - IEICE TRANSACTIONS on Information
Y1 - December 2013
AB - There is a well known Steiner tree algorithm called minimum-cost paths heuristic (MPH), which is used for many multicast network operations and is considered a benchmark for other Steiner tree algorithms. MPH's average case time complexity is O(m(l+nlog n)), where m is the number of end nodes, n is the number of nodes, and l is the number of links in the network, because MPH has to run Dijkstra's algorithm as many times as the number of end nodes. The author recently proposed a Steiner tree algorithm called branch-based multi-cast (BBMC), which produces exactly the same multicast tree as MPH in a constant processing time irrespective of the number of multicast end nodes. However, the theoretical result for the average case time complexity of BBMC was expressed as O(log m(l+nlog n)) and could not accurately reflect the above experimental result. This paper proves that the average case time complexity of BBMC can be shortened to O(l+nlog n), which is independent of the number of end nodes, when there is an upper limit of the node degree, which is the number of links connected to a node. In addition, a new parameter β is applied to BBMC, so that the multicast tree created by BBMC has less links on it. Even though the tree costs increase due to this parameter, the tree cost increase rates are much smaller than the link decrease rates.
ER -
English
