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Finding Sparse Induced Subgraphs of Semirandom Graphs

  • Amin Coja-Oghlan
Conference paper
Part of the Lecture Notes in Computer Science book series (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].

Keywords

Bipartite Graph Random Graph Chromatic Number Random Edge Random Neighbour 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Alon, N., Kahale, N.: Approximating the independence number via the ϑ-function. Math. Programming 80 (1998) 253–264.MathSciNetGoogle Scholar
  2. 2.
    Alon, N., Kahale, N.: A spectral technique for coloring random 3-colorable graphs. SIAM J. Comput. 26 (1997) 1733–1748zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Blum, A., Spencer, J.: Coloring random and semirandom k-colorable graphs. J. of Algorithms 19(2) (1995) 203–234CrossRefMathSciNetGoogle Scholar
  4. 4.
    Coja-Oghlan, A.: On NP-hard semi-random graph problems. Technical report 148, Fachbereich Mathematik der Universität Hamburg (2002)Google Scholar
  5. 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. 6.
    Feige, U., Kilian, J.: Zero knowledge and the chromatic number, J. Comput. System Sci. 57 (1998), 187–199zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Feige, U., Kilian, J.: Heuristics for semirandom graph problems. J. Comput. and System Sci. 63 (2001) 639–671zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Feige, U., Krauthgamer, J.: Finding and certifying a large hidden clique in a semi-random graph. Random Structures & Algorithms 16 (2000) 195–208zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Hℴastad, J.: Clique is hard to approximate within n 1—ɛ. Proc. 37th Annual Symp. on Foundations of Computer Science (1996) 627–636Google Scholar
  10. 10.
    Karger, D., Motwani, R., Sudan, M.: Approximate graph coloring by semidefinite programming. J. Assoc. Comput. Mach. 45 (1998) 246–265zbMATHMathSciNetGoogle Scholar
  11. 11.
    Khanna, S., Linial, N., Safra, S.: On the hardness of approximating the chromatic number. Combinatorica 20 (2000) 393–415zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Lawler, E.L.: A note on the complexity of the chromatic number problem. Information Processing Letters 5 (1976) 66–67zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Mahajan, S., Ramesh, H.: Derandomizing semidefinite programming based approximation algorithms. Proc. 36th IEEE Symp. on Foundations of Computer Science (1995) 162–169Google Scholar
  14. 14.
    Prömel, H. J., Steger, A.: Coloring K l+1-free graphs in linear expected time. Random Structures & Algorithms 3 (1992) 374–402Google Scholar
  15. 15.
    Subramanian, C.: Minimum coloring random and semirandom graphs in polynomial average time. J. of Algorithms 33 (1999) 112–123zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Amin Coja-Oghlan
    • 1
  1. 1.Institut für InformatikHumboldt-Universität zu BerlinBerlinGermany

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