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The paper deals with the shortest path-based in-trees on a grid graph. There a root is supposed to move among all vertices. As such a spanning mobility pattern, root trajectories based on a Hamilton path or cycle are discussed. Along such a trajectory, each vertex randomly selects the next hop on the shortest path to the root. Under those assumptions, this paper shows that a root trajectory termed an S-path provides the minimum expected symmetric difference. Numerical experiments show that another trajectory termed a Right-cycle also provides the minimum result.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E103-A No.9 pp.1071-1077

- Publication Date
- 2020/09/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.2019KEP0003

- Type of Manuscript
- Special Section PAPER (Special Section on Circuits and Systems)

- Category

Yoshihiro KANEKO

Gifu University

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Yoshihiro KANEKO, "The Expected Distance of Shortest Path-Based In-Trees along Spanning Root Mobility on Grid Graph" in IEICE TRANSACTIONS on Fundamentals,
vol. E103-A, no. 9, pp. 1071-1077, September 2020, doi: 10.1587/transfun.2019KEP0003.

Abstract: The paper deals with the shortest path-based in-trees on a grid graph. There a root is supposed to move among all vertices. As such a spanning mobility pattern, root trajectories based on a Hamilton path or cycle are discussed. Along such a trajectory, each vertex randomly selects the next hop on the shortest path to the root. Under those assumptions, this paper shows that a root trajectory termed an S-path provides the minimum expected symmetric difference. Numerical experiments show that another trajectory termed a Right-cycle also provides the minimum result.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2019KEP0003/_p

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@ARTICLE{e103-a_9_1071,

author={Yoshihiro KANEKO, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={The Expected Distance of Shortest Path-Based In-Trees along Spanning Root Mobility on Grid Graph},

year={2020},

volume={E103-A},

number={9},

pages={1071-1077},

abstract={The paper deals with the shortest path-based in-trees on a grid graph. There a root is supposed to move among all vertices. As such a spanning mobility pattern, root trajectories based on a Hamilton path or cycle are discussed. Along such a trajectory, each vertex randomly selects the next hop on the shortest path to the root. Under those assumptions, this paper shows that a root trajectory termed an S-path provides the minimum expected symmetric difference. Numerical experiments show that another trajectory termed a Right-cycle also provides the minimum result.},

keywords={},

doi={10.1587/transfun.2019KEP0003},

ISSN={1745-1337},

month={September},}

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TY - JOUR

TI - The Expected Distance of Shortest Path-Based In-Trees along Spanning Root Mobility on Grid Graph

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1071

EP - 1077

AU - Yoshihiro KANEKO

PY - 2020

DO - 10.1587/transfun.2019KEP0003

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E103-A

IS - 9

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - September 2020

AB - The paper deals with the shortest path-based in-trees on a grid graph. There a root is supposed to move among all vertices. As such a spanning mobility pattern, root trajectories based on a Hamilton path or cycle are discussed. Along such a trajectory, each vertex randomly selects the next hop on the shortest path to the root. Under those assumptions, this paper shows that a root trajectory termed an S-path provides the minimum expected symmetric difference. Numerical experiments show that another trajectory termed a Right-cycle also provides the minimum result.

ER -