  Let $G=(V,E)$ be a simple, unweighted, connected graph. Let $d(u,v)$ denote
the distance between vertices $u,v$. A resolving set of $G$ is a subset $S$ of
$V$ such that knowing the distance from a vertex $v$ to every vertex in $S$
uniquely identifies $v$. The metric dimension of $G$ is defined as the size of
the smallest resolving set of $G$. We define the $k$-truncated resolving set
and $k$-truncated metric dimension of a graph similarly, but with the notion of
distance replaced with $d_k(u,v) := \min(d(u,v),k+1)$.
  In this paper, we demonstrate that computing $k$-truncated dimension of trees
is NP-Hard for general $k$. We then present a polynomial-time algorithm to
compute $k$-truncated dimension of trees when $k$ is a fixed constant.
