Skip to main content
SpringerLink
Log in

Additive Spanners

  • Living reference work entry
  • First Online:
Encyclopedia of Algorithms

Years and Authors of Summarized Original Work

SumOriWork: 2013 Chechik

Problem Definition

A spanner is a subgraph of a given graph that faithfully preserves the pairwise distances of that graph. Formally, an \((\alpha ,\beta )\) spanner of a graph G = (V, E) is a subgraph H of G such that for any pair of nodes x, y, \(\mathbf{dist}(x,y,H) \leq \alpha \cdot \mathbf{dist}(x,y,G)+\beta\), where \(\mathbf{dist}(x,y,H^{{\prime}})\) for a subgraph H ′ is the distance of the shortest path from s to t in \(H^{{\prime}}\). We say that the spanner is additive if α = 1, and if in addition β = O(1), we say that the spanner is purely additive. If β = 0, we say that the spanner is multiplicative; otherwise, we say that the spanner is mixed.

Key Results

This section presents a survey on spanners with a special focus on additive spanners.

Graph spanners were first introduced in [12, 13] in the late 1980s and have been extensively studied since then.

Spanners are used as a key ingredient in many...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Recommended Reading

  1. Aingworth D, Chekuri C, Indyk P, Motwani R (1999) Fast estimation of diameter and shortest paths (without matrix multiplication). SIAM J Comput 28(4):1167–1181

    Article  MATH  MathSciNet  Google Scholar 

  2. Althöfer I, Das G, Dobkin D, Joseph D, Soares J (1993) On sparse spanners of weighted graphs. Discret Comput Geom 9:81–100

    Article  MATH  Google Scholar 

  3. Baswana S, Kavitha T, Mehlhorn K, Pettie S (2005) New constructions of (α, β)-spanners and purely additive spanners. In: Proceedings of the 16th symposium on discrete algorithms (SODA), Vancouver, pp 672–681

    Google Scholar 

  4. Baswana S, Kavitha T, Mehlhorn K, Pettie S (2010) Additive spanners and (α, β)-spanners. ACM Trans Algorithm 7:1–26. A.5

    Google Scholar 

  5. Bollobás B, Coppersmith D, Elkin M (2003) Sparse distance preservers and additive spanners. In: Proceedings of the 14th ACM-SIAM symposium on discrete algorithms (SODA), Baltimore, pp 414–423

    Google Scholar 

  6. Chechik S (2013) Compact routing schemes with improved stretch. In: Proceedings of the 32nd ACM symposium on principles of distributed computing (PODC), Montreal, pp 33–41

    Google Scholar 

  7. Chechik S (2013) New additive spanners. In: Proceedings of the 24th symposium on discrete algorithms (SODA), New Orleans, pp 498–512

    Google Scholar 

  8. Dor D, Halperin S, Zwick U (2000) All-pairs almost shortest paths. SIAM J Comput 29(5):1740–1759

    Article  MATH  MathSciNet  Google Scholar 

  9. Elkin M, Peleg D (2004) (1 +ε, β)-spanner constructions for general graphs. SIAM J Comput 33(3):608–631

    Article  MATH  MathSciNet  Google Scholar 

  10. Erdős P (1964) Extremal problems in graph theory. In: Theory of graphs and its applications. Methuen, London, pp 29–36

    Google Scholar 

  11. Farley AM, Proskurowski A, Zappala D, Windisch K (2004) Spanners and message distribution in networks. Discret Appl Math 137(2):159–171

    Article  MATH  MathSciNet  Google Scholar 

  12. Peleg D, Schäffer AA (1989) Graph spanners. J Graph Theory 13:99–116

    Article  MATH  MathSciNet  Google Scholar 

  13. Peleg D, Ullman JD (1989) An optimal synchronizer for the hypercube. SIAM J Comput 18(4):740–747

    Article  MATH  MathSciNet  Google Scholar 

  14. Peleg D, Upfal E (1989) A trade-off between space and efficiency for routing tables. J ACM 36(3):510–530

    Article  MATH  MathSciNet  Google Scholar 

  15. Pettie S (2009) Low distortion spanners. ACM Trans Algorithms 6(1):1–22

    Article  MathSciNet  Google Scholar 

  16. Roditty L, Thorup M, Zwick U (2005) Deterministic constructions of approximate distance oracles and spanners. In: Proceedings of the 32nd international colloquium on automata, languages and programming (ICALP), Lisbon, pp 261–272

    Google Scholar 

  17. Thorup M, Zwick U (2001) Compact routing schemes. In: Proceedings of the 13th ACM symposium on parallel algorithms and architectures (SPAA), Heraklion, pp 1–10

    Google Scholar 

  18. Thorup M, Zwick U (2005) Approximate distance oracles. J ACM 52(1):1–24

    Article  MATH  MathSciNet  Google Scholar 

  19. Thorup M, Zwick U (2006) Spanners and emulators with sublinear distance errors. In: Proceedings of the 17th ACM-SIAM symposium on discrete algorithms (SODA), Miami, pp 802–809

    Google Scholar 

  20. Woodruff DP (2006) Lower bounds for additive spanners, emulators, and more. In: Proceedings of the 47th IEEE symposium on foundations of computer science (FOCS), Berkeley, pp 389–398

    Google Scholar 

  21. Woodruff DP (2010) Additive spanners in nearly quadratic time. In: Proceedings of the 37th international colloquium on automata, languages and programming (ICALP), Bordeaux, pp 463–474

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Tel-Aviv University, Tel Aviv, Israel

    Shiri Chechik

Authors
  1. Shiri Chechik
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shiri Chechik .

Editor information

Editors and Affiliations

  1. Dept. Electrical Engineering & Computer Science, Northwestern University, Evanston, Illinois, USA

    Ming-Yang Kao

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this entry

Cite this entry

Chechik, S. (2014). Additive Spanners. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-3-642-27848-8_562-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-27848-8_562-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Boston, MA

  • Online ISBN: 978-3-642-27848-8

  • eBook Packages: Springer Reference Computer SciencesReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Search

Navigation