Reliable and Efficient Fixed Rountings on Digraphs

Yoshifumi MANABE; Makoto IMASE; Terunao SONEOKA

Reliable and Efficient Fixed Rountings on Digraphs

Yoshifumi MANABE, Makoto IMASE, Terunao SONEOKA

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The problem of constructing a reliable and efficient routing ρ in a communications network G is considered. The forwarding index ξ(G, ρ), which is defined as the maximum number of routes which pass through each node, is a criterion of network efficiency. The diameter of the surviving route graph D(R(G, ρ)/F), which is defined as the maximum number of surviving routes needed for communication between each pair of nodes if node and edge faults F occur, is a criterion of network reliability. Routings which minimize ξ(G, ρ) and D(R(G, ρ)/F) are needed. In this paper the following are shown: (1) A sufficient condition for k-connected digraphs (k2, 4) to have a routing ρ such that D(R(G, ρ)/F)6 for |F|k. (2) A method of constructing a digraph G and routing ρ₂ such that ξ(G, ρ₂)2log_dn for any number of nodes n and maximum degree d. (3) A method of constructing a digraph G and routing such that ξ(G, ρ₂)3log_dn and D(R(G, )/F)3 for |F|d-1 if nd⁴ and d3.

Publication: IEICE TRANSACTIONS on transactions Vol.E71-E No.12 pp.1212-1220

Publication Date: 1988/12/25

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Type of Manuscript: Special Section PAPER (Special Issue on CAS Karuizawa Workshop)

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Yoshifumi MANABE
Makoto IMASE
Terunao SONEOKA

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Yoshifumi MANABE, Makoto IMASE, Terunao SONEOKA, "Reliable and Efficient Fixed Rountings on Digraphs" in IEICE TRANSACTIONS on transactions, vol. E71-E, no. 12, pp. 1212-1220, December 1988, doi: .
Abstract: The problem of constructing a reliable and efficient routing ρ in a communications network G is considered. The forwarding index ξ(G, ρ), which is defined as the maximum number of routes which pass through each node, is a criterion of network efficiency. The diameter of the surviving route graph D(R(G, ρ)/F), which is defined as the maximum number of surviving routes needed for communication between each pair of nodes if node and edge faults F occur, is a criterion of network reliability. Routings which minimize ξ(G, ρ) and D(R(G, ρ)/F) are needed. In this paper the following are shown: (1) A sufficient condition for k-connected digraphs (k2, 4) to have a routing ρ such that D(R(G, ρ)/F)6 for |F|k. (2) A method of constructing a digraph G and routing ρ₂ such that ξ(G, ρ₂)2log_dn for any number of nodes n and maximum degree d. (3) A method of constructing a digraph G and routing such that ξ(G, ρ₂)3log_dn and D(R(G, )/F)3 for |F|d-1 if nd⁴ and d3.
URL: https://globals.ieice.org/en_transactions/transactions/10.1587/e71-e_12_1212/_p

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@ARTICLE{e71-e_12_1212,
author={Yoshifumi MANABE, Makoto IMASE, Terunao SONEOKA, },
journal={IEICE TRANSACTIONS on transactions},
title={Reliable and Efficient Fixed Rountings on Digraphs},
year={1988},
volume={E71-E},
number={12},
pages={1212-1220},
abstract={The problem of constructing a reliable and efficient routing ρ in a communications network G is considered. The forwarding index ξ(G, ρ), which is defined as the maximum number of routes which pass through each node, is a criterion of network efficiency. The diameter of the surviving route graph D(R(G, ρ)/F), which is defined as the maximum number of surviving routes needed for communication between each pair of nodes if node and edge faults F occur, is a criterion of network reliability. Routings which minimize ξ(G, ρ) and D(R(G, ρ)/F) are needed. In this paper the following are shown: (1) A sufficient condition for k-connected digraphs (k2, 4) to have a routing ρ such that D(R(G, ρ)/F)6 for |F|k. (2) A method of constructing a digraph G and routing ρ₂ such that ξ(G, ρ₂)2log_dn for any number of nodes n and maximum degree d. (3) A method of constructing a digraph G and routing such that ξ(G, ρ₂)3log_dn and D(R(G, )/F)3 for |F|d-1 if nd⁴ and d3.},
keywords={},
doi={},
ISSN={},
month={December},}

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TY - JOUR
TI - Reliable and Efficient Fixed Rountings on Digraphs
T2 - IEICE TRANSACTIONS on transactions
SP - 1212
EP - 1220
AU - Yoshifumi MANABE
AU - Makoto IMASE
AU - Terunao SONEOKA
PY - 1988
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E71-E
IS - 12
JA - IEICE TRANSACTIONS on transactions
Y1 - December 1988
AB - The problem of constructing a reliable and efficient routing ρ in a communications network G is considered. The forwarding index ξ(G, ρ), which is defined as the maximum number of routes which pass through each node, is a criterion of network efficiency. The diameter of the surviving route graph D(R(G, ρ)/F), which is defined as the maximum number of surviving routes needed for communication between each pair of nodes if node and edge faults F occur, is a criterion of network reliability. Routings which minimize ξ(G, ρ) and D(R(G, ρ)/F) are needed. In this paper the following are shown: (1) A sufficient condition for k-connected digraphs (k2, 4) to have a routing ρ such that D(R(G, ρ)/F)6 for |F|k. (2) A method of constructing a digraph G and routing ρ₂ such that ξ(G, ρ₂)2log_dn for any number of nodes n and maximum degree d. (3) A method of constructing a digraph G and routing such that ξ(G, ρ₂)3log_dn and D(R(G, )/F)3 for |F|d-1 if nd⁴ and d3.
ER -