  We investigate higher-order Voronoi diagrams in the city metric. This metric
is induced by quickest paths in the L1 metric in the presence of an
accelerating transportation network of axis-parallel line segments. For the
structural complexity of kth-order city Voronoi diagrams of n point sites, we
show an upper bound of O(k(n - k) + kc) and a lower bound of {\Omega}(n + kc),
where c is the complexity of the transportation network. This is quite
different from the bound O(k(n - k)) in the Euclidean metric. For the special
case where k = n - 1 the complexity in the Euclidean metric is O(n), while that
in the city metric is {\Theta}(nc).
  Furthermore, we develop an O(k^2(n + c) log n)-time iterative algorithm to
compute the kth-order city Voronoi diagram and an O(nc log^2(n + c) log n)-time
divide-and-conquer algorithm to compute the farthest-site city Voronoi diagram.
