Let r be a fixed constant and let H be an r-uniform, D-regular hypergraph on N vertices. Assume further that D > N ǫ for some ǫ > 0. Consider the random greedy algorithm for forming an independent set in H. An independent set is chosen at random by iteratively choosing vertices at random to be in the independent set. At each step we chose a vertex uniformly at random from the collection of vert...

We show that for hypergraphs of bounded edge size, the problem of extending a given list of maximal independent sets is NC-reducible to the computation of an arbitrary maximal independent set for an induced sub-hypergraph. The latter problem is known to be in RNC. In particular, our reduction yields an incremental RNC dualization algorithm for hypergraphs of bounded edge size, a problem previou...

Independent set games are cooperative defined on graphs, where players edges and the value of a coalition is maximum cardinality independent sets in subgraph by coalition. In this paper, we investigate convexity games, as convex possess many nice properties both economically computationally. For introduced Deng et al. [5], provide necessary sufficient characterization for convexity, i.e., every...