research-article

Sparse spanners vs. compact routing

Authors:

Cyril Gavoille,

Christian SommerAuthors Info & Claims

SPAA '11: Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures

Pages 225 - 234

https://doi.org/10.1145/1989493.1989526

Published: 04 June 2011 Publication History

Abstract

Routing with multiplicative stretch 3 (which means that the path used by the routing scheme can be up to three times longer than a shortest path) can be done with routing tables of Θ(√n) bits per node. The space lower bound is due to the existence of dense graphs with large girth. Dense graphs can be sparsified to subgraphs, called spanners, with various stretch guarantees. There are spanners with additive stretch guarantees (some even have constant additive stretch) but only very few additive routing schemes are known.

In this paper, we give reasons why routing in unweighted graphs with additive stretch is difficult in the form of space lower bounds for general graphs and for planar graphs. We prove that any routing scheme using routing tables of size μ bits per node and addresses of poly-logarithmic length has additive stretch Ω(√n/μ) for general graphs, and Ω(√n/μ) for planar graphs. Routing with tables of size O(n^1/3) thus requires a polynomial additive stretch Ω(n^1/3), whereas spanners with average degree O(n^1/3) and constant additive stretch exist for all graphs. Spanners, however sparse they are, do not tell us how to route. These bounds provide the first separation of sparse spanner problems and compact routing problems.

On the positive side, we give an almost tight upper bound: we present the first non-trivial compact routing scheme with o(log²n)-bit addresses, additive stretch O(n^1/3), and table size O(n^1/3) bits for all graphs with linear local tree-width such as planar, bounded-genus, and apex-minor-free graphs. Note: Asymptotic notation in this abstract suppresses factors logarithmic in n.

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Cited By

Huc FJarry ALeone PRolim J(2019)On the efficiency of routing in sensor networksJournal of Parallel and Distributed Computing10.1016/j.jpdc.2012.02.02172:7(889-901)Online publication date: 4-Jan-2019
https://dl.acm.org/doi/10.1016/j.jpdc.2012.02.021
Roditty LTov R(2018)Close to linear space routing schemesDistributed Computing10.1007/s00446-015-0256-529:1(65-74)Online publication date: 26-Dec-2018
https://dl.acm.org/doi/10.1007/s00446-015-0256-5
Sommer C(2014)Shortest-path queries in static networksACM Computing Surveys10.1145/253053146:4(1-31)Online publication date: 1-Mar-2014
https://dl.acm.org/doi/10.1145/2530531
Show More Cited By

Index Terms

Sparse spanners vs. compact routing
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

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cover image ACM Conferences

SPAA '11: Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures

June 2011

404 pages

ISBN:9781450307437

DOI:10.1145/1989493

Co-chairs:
Friedhelm Meyer auf der Heide
University of Paderborn, Germany
,
Rajmohan Rajaraman
Northeastern University, USA

Copyright © 2011 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]

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Published: 04 June 2011

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Cited By

Huc FJarry ALeone PRolim J(2019)On the efficiency of routing in sensor networksJournal of Parallel and Distributed Computing10.1016/j.jpdc.2012.02.02172:7(889-901)Online publication date: 4-Jan-2019
https://dl.acm.org/doi/10.1016/j.jpdc.2012.02.021
Roditty LTov R(2018)Close to linear space routing schemesDistributed Computing10.1007/s00446-015-0256-529:1(65-74)Online publication date: 26-Dec-2018
https://dl.acm.org/doi/10.1007/s00446-015-0256-5
Sommer C(2014)Shortest-path queries in static networksACM Computing Surveys10.1145/253053146:4(1-31)Online publication date: 1-Mar-2014
https://dl.acm.org/doi/10.1145/2530531
Chechik SFatourou PTaubenfeld G(2013)Compact routing schemes with improved stretchProceedings of the 2013 ACM symposium on Principles of distributed computing10.1145/2484239.2484268(33-41)Online publication date: 22-Jul-2013
https://dl.acm.org/doi/10.1145/2484239.2484268
Chen WSommer CTeng SWang Y(2012)A compact routing scheme and approximate distance oracle for power-law graphsACM Transactions on Algorithms (TALG)10.1145/2390176.23901809:1(1-26)Online publication date: 26-Dec-2012
https://dl.acm.org/doi/10.1145/2390176.2390180
Abraham IGavoille C(2011)On approximate distance labels and routing schemes with affine stretchProceedings of the 25th international conference on Distributed computing10.5555/2075029.2075081(404-415)Online publication date: 20-Sep-2011
https://dl.acm.org/doi/10.5555/2075029.2075081
Gavoille CGodfroy QViennot L(2011)Node-Disjoint multipath spanners and their relationship with fault-tolerant spannersProceedings of the 15th international conference on Principles of Distributed Systems10.1007/978-3-642-25873-2_11(143-158)Online publication date: 13-Dec-2011
https://dl.acm.org/doi/10.1007/978-3-642-25873-2_11

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