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 \emph{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.

翻译：我们提出了一种算法，其输入为参数$k$和$r$以及一个秩至多为$r$的超图$H$。该算法要么返回$H$的一个广义超树宽度至多为$4k$的树分解，要么返回'NO'。在后一种情况下，可以保证$H$的超树宽度大于$k$。最重要的是，该算法的运行时间是关于$k$和$r$的\emph{FPT}。该方法可扩展到分数超树宽度，但近似比稍差（$4k+1$而非$4k$）。我们希望本文的结果能开启一个新的研究方向，其目标是为受限类别超图设计计算和近似超树宽度参数的FPT算法。