Competitive Analysis of Minimal Oblivious Routing Algorithms on Hypercubes

Tzuoo-Hawn YEH; Chin-Laung LEI

Competitive Analysis of Minimal Oblivious Routing Algorithms on Hypercubes

Tzuoo-Hawn YEH, Chin-Laung LEI

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We study the performance of oblivious routing algorithms that follow minimal (shortest) paths, referred to as minimal oblivious routing algorithms in this paper, using competitive analysis on a d-dimensional, N = 2^d-node hypercube. We assume that packets are injected into the hypercube arbitrarily and continuously, without any (e.g., probabilistic) assumption on the arrival pattern of the packets. Minimal algorithms reduce the total load in the network in the first place and they preserve locality. First we show that the well known deterministic oblivious routing algorithm, namely, the greedy routing algorithm, has competitive ratio Ω(N^1/2). Then we show a problem lower bound of Ω(N^{log ² (5/4)}/log⁵ N). We also give a natural randomized minimal oblivious routing algorithm whose competitive ratio is close to the problem lower bound we provide.

Publication: IEICE TRANSACTIONS on Information Vol.E84-D No.1 pp.65-75

Publication Date: 2001/01/01

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Category: Algorithms

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Tzuoo-Hawn YEH, Chin-Laung LEI, "Competitive Analysis of Minimal Oblivious Routing Algorithms on Hypercubes" in IEICE TRANSACTIONS on Information, vol. E84-D, no. 1, pp. 65-75, January 2001, doi: .
Abstract: We study the performance of oblivious routing algorithms that follow minimal (shortest) paths, referred to as minimal oblivious routing algorithms in this paper, using competitive analysis on a d-dimensional, N = 2^d-node hypercube. We assume that packets are injected into the hypercube arbitrarily and continuously, without any (e.g., probabilistic) assumption on the arrival pattern of the packets. Minimal algorithms reduce the total load in the network in the first place and they preserve locality. First we show that the well known deterministic oblivious routing algorithm, namely, the greedy routing algorithm, has competitive ratio Ω(N^1/2). Then we show a problem lower bound of Ω(N^{log ² (5/4)}/log⁵ N). We also give a natural randomized minimal oblivious routing algorithm whose competitive ratio is close to the problem lower bound we provide.
URL: https://global.ieice.org/en_transactions/information/10.1587/e84-d_1_65/_p

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@ARTICLE{e84-d_1_65,
author={Tzuoo-Hawn YEH, Chin-Laung LEI, },
journal={IEICE TRANSACTIONS on Information},
title={Competitive Analysis of Minimal Oblivious Routing Algorithms on Hypercubes},
year={2001},
volume={E84-D},
number={1},
pages={65-75},
abstract={We study the performance of oblivious routing algorithms that follow minimal (shortest) paths, referred to as minimal oblivious routing algorithms in this paper, using competitive analysis on a d-dimensional, N = 2^d-node hypercube. We assume that packets are injected into the hypercube arbitrarily and continuously, without any (e.g., probabilistic) assumption on the arrival pattern of the packets. Minimal algorithms reduce the total load in the network in the first place and they preserve locality. First we show that the well known deterministic oblivious routing algorithm, namely, the greedy routing algorithm, has competitive ratio Ω(N^1/2). Then we show a problem lower bound of Ω(N^{log ² (5/4)}/log⁵ N). We also give a natural randomized minimal oblivious routing algorithm whose competitive ratio is close to the problem lower bound we provide.},
keywords={},
doi={},
ISSN={},
month={January},}

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TY - JOUR
TI - Competitive Analysis of Minimal Oblivious Routing Algorithms on Hypercubes
T2 - IEICE TRANSACTIONS on Information
SP - 65
EP - 75
AU - Tzuoo-Hawn YEH
AU - Chin-Laung LEI
PY - 2001
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E84-D
IS - 1
JA - IEICE TRANSACTIONS on Information
Y1 - January 2001
AB - We study the performance of oblivious routing algorithms that follow minimal (shortest) paths, referred to as minimal oblivious routing algorithms in this paper, using competitive analysis on a d-dimensional, N = 2^d-node hypercube. We assume that packets are injected into the hypercube arbitrarily and continuously, without any (e.g., probabilistic) assumption on the arrival pattern of the packets. Minimal algorithms reduce the total load in the network in the first place and they preserve locality. First we show that the well known deterministic oblivious routing algorithm, namely, the greedy routing algorithm, has competitive ratio Ω(N^1/2). Then we show a problem lower bound of Ω(N^{log ² (5/4)}/log⁵ N). We also give a natural randomized minimal oblivious routing algorithm whose competitive ratio is close to the problem lower bound we provide.
ER -