  Given access to the hypergraph through a subset query oracle in the query
model, we give sublinear time algorithms for Hitting-Set with almost tight
parameterized query complexity. In parameterized query complexity, we estimate
the number of queries to the oracle based on the parameter $k$, the size of the
Hitting-Set. The subset query oracle we use in this paper is called Generalized
$d$-partite Independent Set query oracle (GPIS) and it was introduced by Bishnu
et al. (ISAAC'18). GPIS is a generalization to hypergraphs of the Bipartite
Independent Set query oracle (BIS) introduced by Beame et al. (ITCS'18 and
TALG'20) for estimating the number of edges in graphs. Formally, GPIS is
defined as follows: GPIS oracle for a $d$-uniform hypergraph $\mathcal{H}$
takes as input $d$ pairwise disjoint non-empty subsets $A_1, \ldots, A_d$ of
vertices in $\cal H$ and answers whether there is a hyperedge in $\mathcal{H}$
that intersects each set $A_i$, where $i \in \{1, \, 2, \, \ldots, d\}$. } For
$d=2$, the GPIS oracle is nothing but BIS oracle.
  We show that $d$-Hitting-Set, the hitting set problem for $d$-uniform
hypergraphs, can be solved using $\widetilde{\mathcal{O}}_d(k^{d} \log n)$ GPIS
queries. Additionally, we also showed that $d$-Decesion-Hitting-Set, the
decision version of $d$-Hitting-Set can be solved with
$\widetilde{\mathcal{O}}_d\left( \min \left\{ k^d\log n, k^{2d^2} \right\}
\right)$ {\sc GPIS} queries. We complement these parameterized upper bounds
with an almost matching parameterized lower bound that states that any
algorithm that solves $d$-Decesion-Hitting-Set requires $\Omega \left(
\binom{k+d}{d} \right)$ GPIS queries.
