  We consider the problem of finding ``dissimilar'' $k$ shortest paths from $s$
to $t$ in an edge-weighted directed graph $D$, where the dissimilarity is
measured by the minimum pairwise Hamming distances between these paths. More
formally, given an edge-weighted directed graph $D = (V, A)$, two specified
vertices $s, t \in V$, and integers $d, k$, the goal of Dissimilar Shortest
Paths is to decide whether $D$ has $k$ shortest paths $P_1, \dots, P_k$ from
$s$ to $t$ such that $|A(P_i) \mathbin{\triangle} A(P_j)| \ge d$ for distinct
$P_i$ and $P_j$. We design a deterministic algorithm to solve Dissimilar
Shortest Paths with running time $2^{O(3^kdk^2)}n^{O(1)}$, that is, Dissimilar
Shortest Paths is fixed-parameter tractable parameterized by $k + d$. To
complement this positive result, we show that Dissimilar Shortest Paths is
W[1]-hard when parameterized by only $k$ and paraNP-hard parameterized by $d$.
