For a graph G, a function ψ is called a \emph{bar visibility
representation} of G when for each vertex v∈V(G), ψ(v) is a
horizontal line segment (\emph{bar}) and uv∈E(G) iff there is an
unobstructed, vertical, ε-wide line of sight between ψ(u) and
ψ(v). Graphs admitting such representations are well understood (via
simple characterizations) and recognizable in linear time. For a directed graph
G, a bar visibility representation ψ of G, additionally, puts the bar
ψ(u) strictly below the bar ψ(v) for each directed edge (u,v) of
G. We study a generalization of the recognition problem where a function
ψ′ defined on a subset V′ of V(G) is given and the question is whether
there is a bar visibility representation ψ of G with ψ(v)=ψ′(v) for every v∈V′. We show that for undirected graphs this problem
together with closely related problems are \NP-complete, but for certain cases
involving directed graphs it is solvable in polynomial time.Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016