Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

Independent Sets in Random Intersection Graphs

  • Sotiris NikoletseasEmail author
  • Christoforos L. Raptopoulos
  • Paul (Pavlos) Spirakis
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_187

Years and Authors of Summarized Original Work

  • 2004; Nikoletseas, Raptopoulos, Spirakis

Problem Definition

This problem is concerned with the efficient construction of an independent set of vertices (i.e., a set of vertices with no edges between them) with maximum cardinality, when the input is an instance of the uniform random intersection graphs model. This model was introduced by Karoński, Sheinerman, and Singer-Cohen in [4] and Singer-Cohen in [10] and it is defined as follows

Definition 1 (Uniform random intersection graph)

Consider a universe \( { M {=} \{1, 2, \dots, m\} } \)


Existence and efficient construction of independent sets of vertices in general random intersection graphs 
This is a preview of subscription content, log in to check access.

Recommended Reading

  1. 1.
    Alon N, Spencer H (2000) The probabilistic method. WileyzbMATHCrossRefGoogle Scholar
  2. 2.
    Efthymiou C, Spirakis P (2005) On the existence of Hamiltonian cycles in random intersection graphs. In: Proceedings of 32nd international colloquium on automata, languages and programming (ICALP). Springer, Berlin/Heidelberg, pp 690–701Google Scholar
  3. 3.
    Fill JA, Sheinerman ER, Singer-Cohen KB (2000) Random intersection graphs when m = ω(n): an equivalence theorem relating the evolution of the g(n, m, p) and g(n, p)models. Random Struct Algorithms 16(2):156–176MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Karoński M, Scheinerman ER, Singer-Cohen KB (1999) On random intersection graphs: the subgraph problem. Adv Appl Math 8:131–159MathSciNetzbMATHGoogle Scholar
  5. 5.
    Marczewski E (1945) Sur deux propriétés des classes d’ensembles. Fundam Math 33:303–307zbMATHGoogle Scholar
  6. 6.
    Motwani R, Raghavan P (1995) Randomized algorithms. Cambridge University PresszbMATHCrossRefGoogle Scholar
  7. 7.
    Nikoletseas S, Raptopoulos C, Spirakis P (2004) The existence and efficient construction of large independent sets in general random intersection graphs. In: Proceedings of 31st international colloquium on Automata, Languages and Programming (ICALP). Springer, Berlin/Heidelberg, pp 1029–1040. Also in the Theoretical Computer Science (TCS) Journal, accepted, to appear in 2008Google Scholar
  8. 8.
    Raptopoulos C, Spirakis P (2005) Simple and efficient greedy algorithms for Hamiltonian cycles in random intersection graphs. In: Proceedings of the 16th international symposium on algorithms and computation (ISAAC). Springer, Berlin/Heidelberg, pp 493–504Google Scholar
  9. 9.
    Ross S (1995) Stochastic processes. WileyGoogle Scholar
  10. 10.
    Singer-Cohen KB (1995) Random intersection graphs. Ph.D. thesis, John Hopkins University, BaltimoreGoogle Scholar
  11. 11.
    Stark D (2004) The vertex degree distribution of random intersection graphs. Random Struct Algorithms 24:249–258MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Sotiris Nikoletseas
    • 1
    • 3
    Email author
  • Christoforos L. Raptopoulos
    • 2
    • 3
    • 4
  • Paul (Pavlos) Spirakis
    • 5
    • 6
    • 7
  1. 1.Computer Engineering and Informatics Department, University of PatrasPatrasGreece
  2. 2.Computer Science DepartmentUniversity of GenevaGenevaSwitzerland
  3. 3.Computer Technology Institute and Press “Diophantus”PatrasGreece
  4. 4.Research Academic Computer Technology Institute, Greece and Computer Engineering and Informatics DepartmentUniversity of PatrasPatrasGreece
  5. 5.Computer Engineering and Informatics, Research and Academic Computer Technology InstitutePatras UniversityPatrasGreece
  6. 6.Computer ScienceUniversity of LiverpoolLiverpoolUK
  7. 7.Computer Technology Institute (CTI)PatrasGreece