Succinct Geometric Indexes Supporting Point Location Queries

We propose to design 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 data set permuted and stored elsewhere as a sequence. Our first 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) time3 . We also design three variants of this index. The first 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 efficiency 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 succin...

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Prosenjit Bose, Eric Y. Chen, Meng He, Anil Maheshwari, Pat Morin
• Keywords: CORR 2008, Education, Geometric, Point Location, Succinct Geometric Index