NDLI: Optimal Routing in a Small-World Network

Content Provider	Springer Nature Link
Author	Zeng, Jian Yang Hsu, Wen Jing
Copyright Year	2006
Abstract	Substantial research has been devoted to the modelling of the small-world phenomenon that arises in nature as well as human society. Earlier work has focused on the static properties of various small-world models. To examine the routing aspects, Kleinberg proposes a model based on a d-dimensional toroidal lattice with long-range links chosen at random according to the d-harmonic distribution. Kleinberg shows that, by using only local information, the greedy routing algorithm performs in O(lg$^{2}$ n) expected number of hops. We extend Kleinberg’s small-world model by allowing each node x to have two more random links to nodes chosen uniformly and randomly within $$(\lg n)^{\tfrac{2}{d}}$$ Manhattan distance from x. Based on this extended model, we then propose an oblivious algorithm that can route messages between any two nodes in O(lgn) expected number of hops. Our routing algorithm keeps only O((lgn)$^{β+1}$) bits of information on each node, where 1 < β < 2, thus being scalable w.r.t. the network size. To our knowledge, our result is the first to achieve the optimal routing complexity while still keeping a poly-logarithmic number of bits of information stored on each node in the small-world networks.
Starting Page	476
Ending Page	481
Page Count	6
File Format	PDF
ISSN	10009000
Journal	Journal of Computer Science and Technology
Volume Number	21
Issue Number	4
e-ISSN	18604749
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2006-01-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	small-world model augmented local awareness decentralized routing analysis of algorithms distributed systems Computer Science Software Engineering Data Structures, Cryptology and Information Theory Theory of Computation Information Systems Applications (incl.Internet) Artificial Intelligence (incl. Robotics)
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Computational Theory and Mathematics Computer Science Applications Software Hardware and Architecture

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