  When a network is prone to failures, it is very expensive to compute the
shortest paths every time from the scratch. Distance sensitivity oracle
provides this privilege to find the new shortest paths faster and with lower
cost by once pre-computing an oracle in advance. Although several efficient
solutions are proposed in the literature to support the single failure, few
efforts are done to devise an efficient method regarding the case of multiple
failures. In this paper, we present a novel distance sensitivity oracle based
on Markov Tensor Theory \cite{golnari2017markov} to support replacement path
queries $(*,t,\mathcal{F})$ in general directed and weighted networks facing
the set of failures $\mathcal{F}$. In contrast to the existing work, there is
no limitation on maximum failure size supported by our oracle and there is no
need to know the size of failure for constructing the oracle. The
specifications of our oracle are: space size of $O(n^2)$, pre-process time of
$O(n^{\omega})$, where $\omega$ is the exponent of fast matrix multiplication,
and query time of $O(m)$ for answering to replacement path query of
$(*,t,\mathcal{F})$ which computes the replacement (shortest) paths from all
nodes to target $t$ at once. While the computation time for regular shortest
path methods, such as Dijkstra's, is $O(m+nlogn)$ for each query after a
failure, our algorithm can save a considerable computational time when the size
of failure set $|\mathcal{F}|$ is $O(m^{1/\omega})$ or less and the network is
sparse $O(m)<O(nlogn)$.
