Keywords and Synonyms
Existence and efficient construction of independent sets of vertices in general random intersection graphs
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...
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Recommended Reading
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Nikoletseas, S., Raptopoulos, C., Spirakis, P.: 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), pp. 1029–1040. Springer, Berlin Heidelberg (2004) Also in the Theoretical Computer Science (TCS) Journal, accepted, to appear in 2008
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Nikoletseas, S., Raptopoulos, C., Spirakis, P. (2008). Independent Sets in Random Intersection Graphs. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_187
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DOI: https://doi.org/10.1007/978-0-387-30162-4_187
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