research-article

Scale-Free Compact Routing Schemes in Networks of Low Doubling Dimension

Authors:

Goran Konjevod,

Andréa W. Richa,

Donglin XiaAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 12, Issue 3

Article No.: 27, Pages 1 - 29

https://doi.org/10.1145/2876055

Published: 15 June 2016 Publication History

Abstract

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 routing-scheme design: (i) labeled (name-dependent) 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) name-independent 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 ∈ (0, 1) and an n-node edge-weighted network of doubling dimension α ∈ O(loglog n), we present

—a (1 + ϵ)-stretch labeled compact routing scheme with ⌈log n⌉-bit 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 name-independent 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 name-independent routing scheme with o(n^(ϵ/60)²) bits of storage at each node has stretch no less than 9 − ϵ for any ϵ ∈ (0, 8). Therefore, our name-independent routing scheme achieves asymptotically optimal stretch with polylogarithmic storage at each node and packet headers.

Note that both schemes are scale-free in the sense that their space requirements do not depend on the normalized diameter Δ of the network. We also present a simpler nonscale-free (9 + ϵ)-stretch name-independent compact routing scheme with improved space requirements if Δ is polynomial in n.

References

[1]

Ittai Abraham and Cyril Gavoille. 2006. Object location using path separators. In Proceedings of the 25th Annual ACM Symposium on Principles of Distributed Computing (PODC'06). ACM, New York, NY, 188--197.

Digital Library

[2]

Ittai Abraham, Cyril Gavoille, Andrew V. Goldberg, and Dahlia Malkhi. 2006c. Routing in networks with low doubling dimension. In Proceedings of the 26th IEEE International Conference on Distributed Computing Systems (ICDCS'06). IEEE Computer Society, Washington, DC, 75--.

Digital Library

[3]

Ittai Abraham, Cyril Gavoille, and Dahlia Malkhi. 2004. Routing with improved communication-space trade-off. In Distributed Computing: 18th International Conference (DISC'04), Vol. 3274. Springer, 305.

[4]

Ittai Abraham, Cyril Gavoille, and Dahlia Malkhi. 2006a. On space-stretch trade-offs: Lower bounds. In Proceedings of the 18th Annual ACM Symposium on Parallelism in Algorithms and Architectures (SPAA'06). ACM, New York, NY, 207--216.

Digital Library

[5]

Ittai Abraham, Cyril Gavoille, and Dahlia Malkhi. 2006b. On space-stretch trade-offs: Upper bounds. In Proceedings of the 18th Annual ACM Symposium on Parallelism in Algorithms and Architectures (SPAA'06). ACM, New York, NY, 217--224.

Digital Library

[6]

Ittai Abraham and Dahlia Malkhi. 2005. Name independent routing for growth bounded networks. In Proceedings of the 17th Annual ACM Symposium on Parallelism in Algorithms and Architectures (SPAA'05). ACM, New York, NY, 49--55.

Digital Library

[7]

Ittai Abraham, Dahlia Malkhi, and Oren Dobzinski. 2004. LAND: Stretch (1 + &epsi;) locality-aware networks for DHTs. In Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'04). Society for Industrial and Applied Mathematics, Philadelphia, PA, 550--559. http://dl.acm.org/citation.cfm?id=982792.982873

Digital Library

[8]

B. Awerbuch and D. Peleg. 1990. Sparse partitions. In Proceedings of the 31st Annual Symposium on Foundations of Computer Science (SFCS'90). IEEE Computer Society, Washington, DC, 503--513 vol. 2.

Digital Library

[9]

Baruch Awerbuch and David Peleg. 1992. Routing with polynomial communication-space trade-off. SIAM Journal on Discrete Mathematics 5, 2, 151--162.

Digital Library

[10]

Hubert T.-H. Chan, Anupam Gupta, Bruce M. Maggs, and Shuheng Zhou. 2005. On hierarchical routing in doubling metrics. In Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'05). Society for Industrial and Applied Mathematics, Philadelphia, PA, 762--771. http://dl.acm.org/citation.cfm?id=1070432.1070540

Digital Library

[11]

T.-H. Hubert Chan, Michael Dinitz, and Anupam Gupta. 2006. Spanners with slack. In Proceedings of the 14th Conference on Annual European Symposium - Volume 14 (ESA'06). Springer-Verlag, London, UK, 196--207.

Digital Library

[12]

Richard Cole and Lee-Ad Gottlieb. 2006. Searching dynamic point sets in spaces with bounded doubling dimension. In Proceedings of the 38th Annual ACM Symposium on Theory of Computing (STOC'06). ACM, New York, NY, 574--583.

Digital Library

[13]

Lenore J. Cowen. 2001. Compact routing with minimum stretch. Journal of Algorithms 38, 1, 170--183.

Digital Library

[14]

Tamar Eilam, Cyril Gavoille, and David Peleg. 1998. Compact routing schemes with low stretch factor (extended abstract). In Proceedings of the 17th Annual ACM Symposium on Principles of Distributed Computing (PODC'98). ACM, New York, NY, 11--20.

Digital Library

[15]

Pierre Fraigniaud and Cyril Gavoille. 2001. Routing in trees. In Proceedings of the 28th International Colloquium on Automata, Languages and Programming, (ICALP'01). Springer-Verlag, London, UK, 757--772. http://dl.acm.org/citation.cfm?id=646254.684110.

Digital Library

[16]

Cyril Gavoille. 2001. Routing in distributed networks: Overview and open problems. SIGACT News 32, 1, 36--52.

Digital Library

[17]

Cyril Gavoille and David Peleg. 2003. Compact and localized distributed data structures. Distributed Computing 16, 2--3, 111--120.

Digital Library

[18]

Anupam Gupta, Robert Krauthgamer, and James R. Lee. 2003. Bounded geometries, fractals, and low-distortion embeddings. In Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science (FOCS'03). IEEE Computer Society, Washington, DC, 534--. http://dl.acm.org/citation. cfm?id=946243.946308

Digital Library

[19]

Sariel Har-Peled and Manor Mendel. 2005. Fast construction of nets in low dimensional metrics, and their applications. In Proceedings of the 21st Annual Symposium on Computational Geometry (SCG'05). ACM, New York, NY, 150--158.

Digital Library

[20]

David R. Karger and Matthias Ruhl. 2002. Finding nearest neighbors in growth-restricted metrics. In Proceedings of the 34th Annual ACM Symposium on Theory of Computing (STOC'02). ACM, New York, NY, 741--750.

Digital Library

[21]

Jon Kleinberg, Aleksandrs Slivkins, and Tom Wexler. 2009. Triangulation and embedding using small sets of beacons. Journal of the ACM 56, 6, Article 32, 37 pages.

Digital Library

[22]

Goran Konjevod, Andréa W. Richa, and Donglin Xia. 2006. Optimal-stretch name-independent compact routing in doubling metrics. In Proceedings of the 25th Annual ACM Symposium on Principles of Distributed Computing (PODC'06). ACM, New York, NY, 198--207.

Digital Library

[23]

Goran Konjevod, Andréa W. Richa, and Donglin Xia. 2007. Optimal scale-free compact routing schemes in networks of low doubling dimension. In Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'07). Society for Industrial and Applied Mathematics, Philadelphia, PA, 939--948. http://dl.acm.org/citation.cfm?id=1283383.1283484

Digital Library

[24]

Robert Krauthgamer and James R. Lee. 2004. Navigating nets: Simple algorithms for proximity search. In Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'04). Society for Industrial and Applied Mathematics, Philadelphia, PA, 798--807. http://dl.acm.org/citation. cfm?id=982792.982913

Digital Library

[25]

Robert Krauthgamer, James R. Lee, Manor Mendel, and Assaf Naor. 2004. Measured descent: A new embedding method for finite metrics. In Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science. IEEE Computer Society, 434--443.

Digital Library

[26]

David Peleg. 2000. Distributed Computing: A Locality-sensitive Approach. Society for Industrial and Applied Mathematics, Philadelphia, PA.

[27]

Aleksandrs Slivkins. 2005a. Distance estimation and object location via rings of neighbors. In Proceedings of the 24th Annual ACM Symposium on Principles of Distributed Computing (PODC'05). ACM, New York, NY, 41--50.

Digital Library

[28]

Aleksandrs Slivkins. 2005b. Distributed approaches to triangulation and embedding. In Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'05). Society for Industrial and Applied Mathematics, Philadelphia, PA, 640--649. http://dl.acm.org/citation.cfm?id=1070432.1070522.

Digital Library

[29]

Ion Stoica, Robert Morris, David Karger, M. Frans Kaashoek, and Hari Balakrishnan. 2001. Chord: A scalable peer-to-peer lookup service for Internet applications. In Proceedings of the 2001 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communications (SIGCOMM'01). ACM, New York, NY, 149--160.

Digital Library

[30]

Kunal Talwar. 2004. Bypassing the embedding: Algorithms for low dimensional metrics. In Proceedings of the 36th Annual ACM Symposium on Theory of Computing (STOC'04). ACM, New York, NY, 281--290.

Digital Library

[31]

Mikkel Thorup. 2004. Compact oracles for reachability and approximate distances in planar digraphs. Journal of the ACM 51, 6, 993--1024.

Digital Library

[32]

Mikkel Thorup and Uri Zwick. 2001. Compact routing schemes. In Proceedings of the 13th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA'01). ACM, New York, NY, 1--10.

Digital Library

Cited By

Inkulu RKumar P(2021)Routing Among Convex Polygonal Obstacles in the PlaneCombinatorial Optimization and Applications10.1007/978-3-030-92681-6_1(1-11)Online publication date: 17-Dec-2021
https://dl.acm.org/doi/10.1007/978-3-030-92681-6_1
Banyassady BChiu MKorman MMulzer Wvan Renssen ARoeloffzen MSeiferth PStein YVogtenhuber BWillert M(2019)Routing in polygonal domainsComputational Geometry10.1016/j.comgeo.2019.101593(101593)Online publication date: Nov-2019
https://doi.org/10.1016/j.comgeo.2019.101593

Index Terms

Scale-Free Compact Routing Schemes in Networks of Low Doubling Dimension
1. Networks
  1. Network protocols
    1. Network layer protocols
      1. Routing protocols
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis
      1. Routing and network design problems
    2. Graph algorithms analysis
      1. Sparsification and spanners

Recommendations

Compact routing with slack in low doubling dimension
PODC '07: Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
We consider the problem of compact routing with slack in networks of low doubling dimension. Namely, we seek name-independent routing schemes with (1+ε) stretch and polylogarithmic storage at each node: since existing lower bound precludes such a scheme,...
Optimal-stretch name-independent compact routing in doubling metrics
PODC '06: Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing

We consider the problem of name-independent routing in doubling metrics. A doubling metric is a metric space whose doubling dimension is a constant, where the doubling dimension of a metric space is the least value α such that any ball of radius r can ...
Compact routing design in networks of low doubling dimension

Comments

Information & Contributors

Information

Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 12, Issue 3

June 2016

408 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/2930058

Editor:
Aravind Srinivasan
University of Maryland, USA

Issue’s Table of Contents

Copyright © 2016 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 15 June 2016

Accepted: 01 January 2016

Revised: 01 October 2008

Received: 01 April 2007

Published in TALG Volume 12, Issue 3

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article
Research
Refereed

Funding Sources

NSF grant CCF

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

2
Total Citations
View Citations
155
Total Downloads

Downloads (Last 12 months)8
Downloads (Last 6 weeks)5

Reflects downloads up to 09 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

Inkulu RKumar P(2021)Routing Among Convex Polygonal Obstacles in the PlaneCombinatorial Optimization and Applications10.1007/978-3-030-92681-6_1(1-11)Online publication date: 17-Dec-2021
https://dl.acm.org/doi/10.1007/978-3-030-92681-6_1
Banyassady BChiu MKorman MMulzer Wvan Renssen ARoeloffzen MSeiferth PStein YVogtenhuber BWillert M(2019)Routing in polygonal domainsComputational Geometry10.1016/j.comgeo.2019.101593(101593)Online publication date: Nov-2019
https://doi.org/10.1016/j.comgeo.2019.101593

View Options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Issue’s Table of Contents