Two-Guard Walkability of Simple Polygons

L. H. Tseng, P. Heffernan, D. T. Lee
1998 International journal of computational geometry and applications  
A pair of points s and g on the boundary of a simple polygon P admits a walk if two guards can simultaneously walk along the two boundary chains of P from s to g such that they are always visible to each other. The walk is a counter-walk if one guard moves from s to g while the other moves from g to s in the same direction along the boundary and they are always visible to each other. The (counter-)walk is straight if no backtracking is necessary during the (counter-)walk. In this paper, we show
more » ... that, given a polygon with n vertices, to test if there exists (s; g) that admits a (straight) (counter-)walk can be solved in time O(n log n) and in linear space. Also we compute all (s; g)'s that admit a (straight) walk in O(n log n) time and all vertex pairs that admit a (straight) counter-walk in O(n log n + m), where m is O(n 2 ).
doi:10.1142/s0218195998000060 fatcat:b4vf6fitljb7zlqwaqzn34374y