Reachable region query and its applications.

In this paper we study the reachable region queries for objects moving in obstacle space. Loosely speaking, given any one of moving objects and many other information, we are asked to return the whole region in which each location has the non-zero probability to be reachable for the moving object. To solve this problem, this paper presents an efficient algorithm that runs in O(nlog n) time and consumes O(nlog n) space, where n is the number of vertices of obstacles. Moreover, this paper establishes the lower bound for the proposed problem, showing that our solution essentially is optimal in terms of random access memory (RAM) model. Empirical study based on both real and synthetic datasets demonstrates the effectiveness and efficiency of our solution.