Add to ORKGWe consider the problem of finding deterministically a large independent set of guaranteed size in a hypergraph on n vertices and with m edges. With respect to the Turan bound, the quality of our solutions is for hypergraphs with not too many small cycles by a logarithmic factor in the input size better. The algorithms are fast; they often have a running time of O(m)+o(n"3). Indeed, the denser the hypergraphs are the more close are the running times to the linear ones. This gives for the first time for some combinatorial problems algorithmic solutions with state-of-the-art quality, solutions of which so far only the existence was known. In some cases, the corresponding upper bounds match the lower bounds up to constant factors. The inv...