Skip to main content
SpringerLink
Log in

Finding Sparse Induced Subgraphs of Semirandom Graphs

  • Conference paper
  • First Online:
Randomization and Approximation Techniques in Computer Science (RANDOM 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2483))

Abstract

The aim of this paper is to present an SDP-based algorithm for finding a sparse induced subgraph of order Θ(n) hidden in a semi-random graph of order n. As an application we obtain an algorithm that requires only O(n) random edges in order to k-color a semirandom k-colorable graph within polynomial expected time, thereby extending the results of Feige and Kilian [7] and of Subramanian [15].

Research supported by the Deutsche Forschungsgemeinschaft (grant DFG FOR 413/1-1)

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alon, N., Kahale, N.: Approximating the independence number via the ϑ-function. Math. Programming 80 (1998) 253–264.

    MathSciNet  Google Scholar 

  2. Alon, N., Kahale, N.: A spectral technique for coloring random 3-colorable graphs. SIAM J. Comput. 26 (1997) 1733–1748

    Article  MATH  MathSciNet  Google Scholar 

  3. Blum, A., Spencer, J.: Coloring random and semirandom k-colorable graphs. J. of Algorithms 19(2) (1995) 203–234

    Article  MathSciNet  Google Scholar 

  4. Coja-Oghlan, A.: On NP-hard semi-random graph problems. Technical report 148, Fachbereich Mathematik der Universität Hamburg (2002)

    Google Scholar 

  5. Coja-Oghlan, A.: Zum Färben k-färbbarer semizufälliger Graphen in erwarteter Polynomzeit mittels Semidefiniter Programmierung. Technical report 141, Fachbereich Mathematik der Universität Hamburg (2002); an extended abstract version is to appear in Proc. 27th. Int. Symp. on Math. Found. of Comp. Sci. (2002)

    Google Scholar 

  6. Feige, U., Kilian, J.: Zero knowledge and the chromatic number, J. Comput. System Sci. 57 (1998), 187–199

    Article  MATH  MathSciNet  Google Scholar 

  7. Feige, U., Kilian, J.: Heuristics for semirandom graph problems. J. Comput. and System Sci. 63 (2001) 639–671

    Article  MATH  MathSciNet  Google Scholar 

  8. Feige, U., Krauthgamer, J.: Finding and certifying a large hidden clique in a semi-random graph. Random Structures & Algorithms 16 (2000) 195–208

    Article  MATH  MathSciNet  Google Scholar 

  9. Hℴastad, J.: Clique is hard to approximate within n 1—ɛ. Proc. 37th Annual Symp. on Foundations of Computer Science (1996) 627–636

    Google Scholar 

  10. Karger, D., Motwani, R., Sudan, M.: Approximate graph coloring by semidefinite programming. J. Assoc. Comput. Mach. 45 (1998) 246–265

    MATH  MathSciNet  Google Scholar 

  11. Khanna, S., Linial, N., Safra, S.: On the hardness of approximating the chromatic number. Combinatorica 20 (2000) 393–415

    Article  MATH  MathSciNet  Google Scholar 

  12. Lawler, E.L.: A note on the complexity of the chromatic number problem. Information Processing Letters 5 (1976) 66–67

    Article  MATH  MathSciNet  Google Scholar 

  13. Mahajan, S., Ramesh, H.: Derandomizing semidefinite programming based approximation algorithms. Proc. 36th IEEE Symp. on Foundations of Computer Science (1995) 162–169

    Google Scholar 

  14. Prömel, H. J., Steger, A.: Coloring K l+1-free graphs in linear expected time. Random Structures & Algorithms 3 (1992) 374–402

    Google Scholar 

  15. Subramanian, C.: Minimum coloring random and semirandom graphs in polynomial average time. J. of Algorithms 33 (1999) 112–123

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Amin Coja-Oghlan

Authors
  1. Amin Coja-Oghlan
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Centre Universitaire d’Informatique, University of Geneva, 24, Rue Général Dufour, 1211, Genéve 4, Switzerland

    José D. P. Rolim

  2. Harvard University, DEAS, Maxwell Dworkin 337, 33 Oxford Street, Cambridge, MA, 02138, USA

    Salil Vadhan

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Coja-Oghlan, A. (2002). Finding Sparse Induced Subgraphs of Semirandom Graphs. In: Rolim, J.D.P., Vadhan, S. (eds) Randomization and Approximation Techniques in Computer Science. RANDOM 2002. Lecture Notes in Computer Science, vol 2483. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45726-7_12

Download citation

  • DOI: https://doi.org/10.1007/3-540-45726-7_12

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44147-2

  • Online ISBN: 978-3-540-45726-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation