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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)}/log^{5} *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

- Publicized

- Online ISSN

- DOI

- Type of Manuscript
- PAPER

- 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)}/log^{5} *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)}/log^{5} *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)}/log^{5} *N*). We also give a natural randomized minimal oblivious routing algorithm whose competitive ratio is close to the problem lower bound we provide.

ER -