ScaleFree Compact Routing Schemes in Networks of Low Doubling Dimension
Abstract
In this work, we consider compact routing schemes in networks of low doubling dimension, where the doubling dimension is the least value α such that any ball in the network can be covered by at most 2 ^{α} balls of half radius. There are two variants of routingscheme design: (i) labeled (namedependent) routing, in which the designer is allowed to rename the nodes so that the names (labels) can contain additional routing information, for example, topological information; and (ii) nameindependent routing, which works on top of the arbitrary original node names in the network, that is, the node names are independent of the routing scheme. In this article, given any constant ε ϵ (0, 1) and an nnode edgeweighted network of doubling dimension α ϵ O(loglog n), we present —a (1 + ε)stretch labeled compact routing scheme with Γlog nbit routing labels, O(log ^{2} n/loglog n)bit packet headers, and ((1/ε) ^{O(α)} log ^{3} n)bit routing information at each node; —a (9 + ε)stretch nameindependent compact routing scheme with O(log ^{2} n/loglog n)bit packet headers, and ((1/ε) ^{O(α)} log ^{3} n)bit routing information at each node. In addition, we prove a lower bound: any nameindependent routing scheme with o(n ^{(ε/60)2}) bitsmore »
 Authors:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Arizona State Univ., Tempe, AZ (United States)
 Google, Kirkland, WA (United States)
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1390021
 Report Number(s):
 LLNLJRNL738008
Journal ID: ISSN 15496325
 Grant/Contract Number:
 AC5207NA27344
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 ACM Transactions on Algorithms
 Additional Journal Information:
 Journal Volume: 12; Journal Issue: 3; Journal ID: ISSN 15496325
 Publisher:
 Association for Computing Machinery
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Scale free; labeled routing; nameindependent routing; compact routing; doubling dimension
Citation Formats
Konjevod, Goran, Richa, Andréa W., and Xia, Donglin. ScaleFree Compact Routing Schemes in Networks of Low Doubling Dimension. United States: N. p., 2016.
Web. doi:10.1145/2876055.
Konjevod, Goran, Richa, Andréa W., & Xia, Donglin. ScaleFree Compact Routing Schemes in Networks of Low Doubling Dimension. United States. doi:10.1145/2876055.
Konjevod, Goran, Richa, Andréa W., and Xia, Donglin. 2016.
"ScaleFree Compact Routing Schemes in Networks of Low Doubling Dimension". United States.
doi:10.1145/2876055. https://www.osti.gov/servlets/purl/1390021.
@article{osti_1390021,
title = {ScaleFree Compact Routing Schemes in Networks of Low Doubling Dimension},
author = {Konjevod, Goran and Richa, Andréa W. and Xia, Donglin},
abstractNote = {In this work, we consider compact routing schemes in networks of low doubling dimension, where the doubling dimension is the least value α such that any ball in the network can be covered by at most 2α balls of half radius. There are two variants of routingscheme design: (i) labeled (namedependent) routing, in which the designer is allowed to rename the nodes so that the names (labels) can contain additional routing information, for example, topological information; and (ii) nameindependent routing, which works on top of the arbitrary original node names in the network, that is, the node names are independent of the routing scheme. In this article, given any constant ε ϵ (0, 1) and an nnode edgeweighted network of doubling dimension α ϵ O(loglog n), we present —a (1 + ε)stretch labeled compact routing scheme with Γlog nbit routing labels, O(log2 n/loglog n)bit packet headers, and ((1/ε)O(α) log3 n)bit routing information at each node; —a (9 + ε)stretch nameindependent compact routing scheme with O(log2 n/loglog n)bit packet headers, and ((1/ε)O(α) log3 n)bit routing information at each node. In addition, we prove a lower bound: any nameindependent routing scheme with o(n(ε/60)2) bits of storage at each node has stretch no less than 9  ε for any ε ϵ (0, 8). Therefore, our nameindependent routing scheme achieves asymptotically optimal stretch with polylogarithmic storage at each node and packet headers. Note that both schemes are scalefree in the sense that their space requirements do not depend on the normalized diameter Δ of the network. Finally, we also present a simpler nonscalefree (9 + ε)stretch nameindependent compact routing scheme with improved space requirements if Δ is polynomial in n.},
doi = {10.1145/2876055},
journal = {ACM Transactions on Algorithms},
number = 3,
volume = 12,
place = {United States},
year = 2016,
month = 6
}

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