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 quite some 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 can contain arbitrary large holes but not large antiholes . Moreover, we obtain two algorithmic results which are interesting from a practical perspective . We devise a fast  shortest path algorithm on arbitrary induced subgraphs of terrain visibility graphs and a polynomial-time algorithm for Dominating Set on special terrain visibility graphs (called funnel visibility graphs).
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 arbitrary induced subgraphs of terrain visibility graphs and a polynomial-time algorithm for Dominating Set on special terrain visibility graphs (called funnel visibility graphs).
D
quite some
R
can contain arbitrary large holes but not large antiholes
cannot contain antiholes of size larger than five
D
which are interesting from a practical perspective
A
output-sensitive
R
Dominating Set
Dominating Set