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The order/degree problem consists of finding the smallest diameter graph for a given order and degree. Such a graph is beneficial for designing low-latency networks with high performance for massively parallel computers. The average shortest path length (ASPL) of a graph has an influence on latency. In this paper, we propose a novel order adjustment approach. In the proposed approach, we search for Cayley graphs of the given degree that are close to the given order. We then adjust the order of the best Cayley graph to meet the given order. For some order and degree pairs, we explain how to derive the smallest known graphs from the Graph Golf 2016 and 2017 competitions.

- Publication
- IEICE TRANSACTIONS on Information Vol.E101-D No.12 pp.2908-2915

- Publication Date
- 2018/12/01

- Publicized
- 2018/09/18

- Online ISSN
- 1745-1361

- DOI
- 10.1587/transinf.2018PAP0008

- Type of Manuscript
- Special Section PAPER (Special Section on Parallel and Distributed Computing and Networking)

- Category
- Graph Algorithms

Teruaki KITASUKA

Hiroshima University

Takayuki MATSUZAKI

Kumamoto University

Masahiro IIDA

Kumamoto 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.

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Teruaki KITASUKA, Takayuki MATSUZAKI, Masahiro IIDA, "Order Adjustment Approach Using Cayley Graphs for the Order/Degree Problem" in IEICE TRANSACTIONS on Information,
vol. E101-D, no. 12, pp. 2908-2915, December 2018, doi: 10.1587/transinf.2018PAP0008.

Abstract: The order/degree problem consists of finding the smallest diameter graph for a given order and degree. Such a graph is beneficial for designing low-latency networks with high performance for massively parallel computers. The average shortest path length (ASPL) of a graph has an influence on latency. In this paper, we propose a novel order adjustment approach. In the proposed approach, we search for Cayley graphs of the given degree that are close to the given order. We then adjust the order of the best Cayley graph to meet the given order. For some order and degree pairs, we explain how to derive the smallest known graphs from the Graph Golf 2016 and 2017 competitions.

URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2018PAP0008/_p

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@ARTICLE{e101-d_12_2908,

author={Teruaki KITASUKA, Takayuki MATSUZAKI, Masahiro IIDA, },

journal={IEICE TRANSACTIONS on Information},

title={Order Adjustment Approach Using Cayley Graphs for the Order/Degree Problem},

year={2018},

volume={E101-D},

number={12},

pages={2908-2915},

abstract={The order/degree problem consists of finding the smallest diameter graph for a given order and degree. Such a graph is beneficial for designing low-latency networks with high performance for massively parallel computers. The average shortest path length (ASPL) of a graph has an influence on latency. In this paper, we propose a novel order adjustment approach. In the proposed approach, we search for Cayley graphs of the given degree that are close to the given order. We then adjust the order of the best Cayley graph to meet the given order. For some order and degree pairs, we explain how to derive the smallest known graphs from the Graph Golf 2016 and 2017 competitions.},

keywords={},

doi={10.1587/transinf.2018PAP0008},

ISSN={1745-1361},

month={December},}

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TY - JOUR

TI - Order Adjustment Approach Using Cayley Graphs for the Order/Degree Problem

T2 - IEICE TRANSACTIONS on Information

SP - 2908

EP - 2915

AU - Teruaki KITASUKA

AU - Takayuki MATSUZAKI

AU - Masahiro IIDA

PY - 2018

DO - 10.1587/transinf.2018PAP0008

JO - IEICE TRANSACTIONS on Information

SN - 1745-1361

VL - E101-D

IS - 12

JA - IEICE TRANSACTIONS on Information

Y1 - December 2018

AB - The order/degree problem consists of finding the smallest diameter graph for a given order and degree. Such a graph is beneficial for designing low-latency networks with high performance for massively parallel computers. The average shortest path length (ASPL) of a graph has an influence on latency. In this paper, we propose a novel order adjustment approach. In the proposed approach, we search for Cayley graphs of the given degree that are close to the given order. We then adjust the order of the best Cayley graph to meet the given order. For some order and degree pairs, we explain how to derive the smallest known graphs from the Graph Golf 2016 and 2017 competitions.

ER -