Abstract

We describe a new technique for dynamically maintaining the trapezoidal decomposition of a connected planar map M with 7 ~ vertices, and apply it to the development of a unified dynamic data structure that supports point-location, ray-shooting, and shortest-path queries in M. The space requirement is O(nlog n). Point-location queries take time O(log 7~). Ray-shooting and shortest-path queries take time O(log3 TZ) (plus O(k) time if the k edges of the shortest path are reported in addition to its length). Updates consist of insertions and deletions of vertices and edges, and take O(log3 n) time (amortized for vertex updates).

Citations