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We propose an algorithm whose input are parameters $k$ and $r$ and ahypergraph $H$ of rank at most $r$. The algorithm either returns a treedecomposition of $H$ of generalized hypertree width at most $4k$ or 'NO'. Inthe latter case, it is guaranteed that the hypertree width of $H$ is greaterthan $k$. Most importantly, the runtime of the algorithm is \emph{FPT} in $k$and $r$. The approach extends to fractional hypertree width with a slightlyworse approximation ($4k+1$ instead of $4k$). We hope that the results of thispaper will give rise to a new research direction whose aim is design of FPTalgorithms for computation and approximation of hypertree width parameters forrestricted classes of hypergraphs.

Constant ratio FPT approximation of hypertree width parameters for hypergraphs of bounded rank