shortest path queries in simple polygons.

Let P be a simple polygon of n vertices. We consider two-point L1 shortest path queries in P. We build a data structure of O(n) size in O(n) time such that given any two query points s and t, the length of an L1 shortest path from s to t in P can be computed in O(log⁡n) time, or in O(1) time if both s and t are vertices of P, and an actual shortest path can be output in additional linear time in the number of edges of the path. To achieve the result, we propose a mountain decomposition of simple polygons, which may be interesting in its own right. Most importantly, our approach is much simpler than the previous work on this problem.