  We study terrain visibility graphs, a well-known graph class closely related
to polygon visibility graphs in computational geometry, for which a precise
graph-theoretical characterization is still unknown. Over the last decade,
terrain visibility graphs attracted attention in the context of time series
analysis with various practical applications in areas such as physics,
geography and medical sciences. We make progress in understanding terrain
visibility graphs by providing several graph-theoretic results. For example, we
show that they cannot contain antiholes of size larger than five. Moreover, we
obtain two algorithmic results. We devise a fast output-sensitive shortest path
algorithm on terrain-like graphs and a polynomial-time algorithm for
\textsc{Dominating Set} on special terrain visibility graphs (called funnel
visibility graphs).
