Abstract

We present a data structure that can store a set of disjoint fat objects in d-space such that point location and bounded-size range searching with arbitrarily-shaped ranges can be performed efficiently. The structure can deal with either arbitrary (fat) convex objects or non-convex polytopes. The multi-purpose data structure supports point location and range searching queries in time O(log d\Gamma1 n) and requires O(n log d\Gamma1 n) storage, after O(n log d\Gamma1 n log log n) preprocessing. The data structure and query algorithm are rather simple. 1 Introduction Fatness turns out to be an interesting phenomenon in computational geometry. Several papers present surprising combinatorial complexity reductions [3, 15, 22, 26, 32] and efficiency gains for algorithms [1, 4, 19, 28, 33] if the objects under consideration have a certain fatness. Fat objects are compact to some extent, rather than long and thin. Fatness is a realistic assumption, since in many practical instances of ...

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