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The algorithmic aspects of uncrowded hypergraphs

We 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 better for hypergraphs with not too many small cycles by a logarithmic factor in the input size. The algorithms are fast; they often have a running time of O(m) + o(n3). Indeed, the denser the hypergraphs are the closer the running times are to the linear times. For the first time, this gives for some combinatorial problems algorithmic solutions with state-of-the-art quality, solutions of which only the existence was known to date. In some cases, the corresponding upper bounds match the lower bounds up to constant factors. The involved concepts are uncrowded hypergraphs.