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 \( { M {=} \{1, 2, \dots, m\} } \) of elements and a set of vertices \( { V {=} \{ v_1, v_2, \dots, v_n\!\} } \). If one assigns independently to each vertex \( { v_j, j = 1, 2, \dots, n } \), a subset \( { S_{v_j} } \) of M by choosing each element independently with probability p and puts an edge between two vertices \( { v_{j_1}, v_{j_2} } \) if and only if \( { S_{v_{j_1}} \cap S_{v_{j_2}} \neq \emptyset } \), then the resulting graph is...
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Recommended Reading
Alon N, Spencer H (2000) The probabilistic method. Wiley
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 690–701
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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 493–504
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Nikoletseas, S., Raptopoulos, C.L., Spirakis, P.(. (2016). Independent Sets in Random Intersection Graphs. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_187
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