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 (Gn,m,p) which includes the model of  (the “uniform”
random intersection graphs model) 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.