Partially walking a polygon

Abstract Deciding two-guard walkability of an n-sided polygon is a well-understood problem. We study the following more general question: How far can two guards reach from a given source vertex while staying mutually visible, in the (more realistic) case that the polygon is not entirely walkable? There can be Θ ( n ) such maximal walks, and we show how to find all of them in O ( n log ⁡ n ) time.