Competitive Analysis of Minimal Oblivious Routing Algorithms on Hypercubes

Tzuoo-Hawn YEH  Chin-Laung LEI  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E84-D   No.1   pp.65-75
Publication Date: 2001/01/01
Online ISSN: 
DOI: 
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Algorithms
Keyword: 
routing algorithms,  minimal oblivious routing algorithms,  hypercubes,  competitive analysis,  

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Summary: 
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 = 2d-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(N1/2). Then we show a problem lower bound of Ω(Nlog 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.