Approximating layout problems on random geometric graphs
Journal of Algorithms
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Short Vertex Disjoint Paths and Multiconnectivity in Random Graphs: Reliable Network Computing
ICALP '94 Proceedings of the 21st International Colloquium on Automata, Languages and Programming
A Random Graph Model for Optical Networks of Sensors
IEEE Transactions on Mobile Computing
On Random Intersection Graphs: The Subgraph Problem
Combinatorics, Probability and Computing
Expander properties and the cover time of random intersection graphs
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Algorithms for wireless sensor networks: design, analysis and experimental evaluation
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
Selected combinatorial properties of random intersection graphs
Algebraic Foundations in Computer Science
A guided tour in random intersection graphs
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
Constructions of independent sets in random intersection graphs
Theoretical Computer Science
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We investigate the existence and efficient algorithmic construction of close to optimal independent sets in random models of intersection graphs. In particular, (a) we propose a new model for random intersection graphs (G"n","m","p"-) which includes the model of [M. Karonski, E.R. Scheinerman, K.B. Singer-Cohen, On random intersection graphs: The subgraph problem, Combinatorics, Probability and Computing journal 8 (1999), 131-159] (the ''uniform'' random intersection graph models) as an important special case. We also define an interesting variation of the model of random intersection graphs, similar in spirit to random regular graphs. (b) For this model we derive exact formulae for the mean and variance of the number of independent sets of size k (for any k) in the graph. (c) We then propose and analyse three algorithms for the efficient construction of large independent sets in this model. The first two are variations of the greedy technique while the third is a totally new algorithm. Our algorithms are analysed for the special case of uniform random intersection graphs. Our analyses show that these algorithms succeed in finding close to optimal independent sets for an interesting range of graph parameters.