Point Location in Fat Subdivisions

Abstract We study the point location problem in fat subdivisions in d -dimensional space. Informally speaking, subdivisions are called fat if no cell has long and skinny parts. It is shown that, assuming the complexity of each cell is bounded by a constant, point location queries in such subdivisions can be performed in a very simple way in time O(log d -1 n ) with a data structure using O( n log d -1 n ) storage. The problem is also studied in the situation where the largest cell is only a factor R larger than the smallest cell. In this case we obtain a solution with only O(log R ) query time using linear storage.