This paper deals with approximations of maximum independent sets in non-uniform hypergraphs of low degree. We obtain the first performance ratio that is sublinear in terms of the maximum or average degree of the hypergraph. We extend this to the weighted case and give a O(D̄ log log D̄/ log D̄) bound, where D̄ is the average weighted degree in a hypergraph, matching the best bounds known for the sp...

In this paper we deal with the on-line maximum independent set and we propose a probabilistic O(logn)-competitive algorithm for chordal and interval graphs, proving that the same ratio is a lower bound of the problem. The relation of the on-line maximum independent set with the on-line admission control, allows us to obtain as particular case, an O(logn)-competitive algorithm for the on-line ad...