The power of geometric duality
BIT - Ellis Horwood series in artificial intelligence
Planar point location using persistent search trees
Communications of the ACM
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Journal of Algorithms
An implicit data structure supporting insertion, deletion, and search in O(log:OS2:OEn) time
Journal of Computer and System Sciences
Optimal point location in a monotone subdivision
SIAM Journal on Computing
Fast algorithms for shortest paths in planar graphs, with applications
SIAM Journal on Computing
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
A pedestrian approach to ray shooting: shoot a ray, take a walk
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Linear Algorithms for Partitioning Embedded Graphs of BoundedGenus
SIAM Journal on Discrete Mathematics
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Efficient suffix trees on secondary storage
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Methods for achieving fast query times in point location data structures
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
On the exact worst case query complexity of planar point location
Journal of Algorithms
Representing dynamic binary trees succinctly
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
High-order entropy-compressed text indexes
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Towards in-place geometric algorithms and data structures
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Expected asymptotically optimal planar point location
Computational Geometry: Theory and Applications - Special issue on the 10th fall workshop on computational geometry
Orderly Spanning Trees with Applications
SIAM Journal on Computing
Structuring labeled trees for optimal succinctness, and beyond
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Optimal succinct representations of planar maps
Proceedings of the twenty-second annual symposium on Computational geometry
Planar Point Location in Sublogarithmic Time
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Succinct ordinal trees with level-ancestor queries
ACM Transactions on Algorithms (TALG)
When indexing equals compression: Experiments with compressing suffix arrays and applications
ACM Transactions on Algorithms (TALG)
Succinct indexes for strings, binary relations and multi-labeled trees
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Succinct indexable dictionaries with applications to encoding k-ary trees, prefix sums and multisets
ACM Transactions on Algorithms (TALG)
Adaptive searching in succinctly encoded binary relations and tree-structured documents
Theoretical Computer Science
Optimal Expected-Case Planar Point Location
SIAM Journal on Computing
In-place 2-d nearest neighbor search
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Space-efficient static trees and graphs
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Succinct representation of labeled graphs
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Succinct representation of triangulations with a boundary
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
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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 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) time. We also design three variants of this index. The first supports point location using lg n + 2&sqrt;lg n + O(lg 1/4 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(nlg n) bits, while saving drastic amounts of space. We generalize our succinct geometric index to planar subdivisions, and design indexes for other types of queries. Finally, we apply our techniques to design the first implicit data structures that support point location in O(lg2 n) time.