FPT algoritms providing constant ratio approximation of hypertree width parameters for hypergraphs of bounded rank

12/27/2022

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by   Igor Razgon, et al.

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We propose an algorithm whose input are parameters k and r and a hypergraph H of rank at most r. The algorithm either returns a tree decomposition of H of generalized hypertree width at most 4k or 'NO'. In the latter case, it is guaranteed that the hypertree width of H is greater than k. Most importantly, the runtime of the algorithm is FPT in k and r. The approach extends to fractional hypertree width with a slightly worse approximation (4k+1 instead of 4k). We hope that the results of this paper will give rise to a new research direction whose aim is design of FPT algorithms for computation and approximation of hypertree width parameters for restricted classes of hypergraphs.