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Succinct geometric indexes supporting point location queries

Succinct Geometric Indexes Supporting Point Location Queries PROSENJIT BOSE, Carleton University ERIC Y. CHEN, Google Inc. MENG HE, University of Waterloo ANIL MAHESHWARI and PAT MORIN, Carleton University We propose designing data structures called succinct geometric indexes of negligible space (more precisely, o(n) bits) that support geometric queries in optimal time, by taking advantage of the n points in the dataset permuted and stored elsewhere as a sequence. Our rst and main result is a succinct geometric index that can answer point location queries, a fundamental problem in computational geometry, on planar triangulations in O(lg n) time. We also design three variants of this index. The rst supports point location using lg n+2 lg n+ O(lg1/4 n) point-line comparisons. The second supports point location in o(lg n) time when the coordinates are integers bounded by U . The last variant can answer point location queries in O(H + 1) expected time, where H is the entropy of the query distribution. These results match the query ef ciency of previous point location structures that occupy O(n) words or O(n lg n) bits, while saving drastic amounts of space. We generalize our succinct geometric index to planar subdivisions, and design http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Algorithms (TALG) Association for Computing Machinery

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