Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
The BANG file: A new kind of grid file
SIGMOD '87 Proceedings of the 1987 ACM SIGMOD international conference on Management of data
Space-time trade-offs for orthogonal range queries
SIAM Journal on Computing
The design and analysis of spatial data structures
The design and analysis of spatial data structures
Lower bounds for orthogonal range searching: I. The reporting case
Journal of the ACM (JACM)
The R*-tree: an efficient and robust access method for points and rectangles
SIGMOD '90 Proceedings of the 1990 ACM SIGMOD international conference on Management of data
The hB-tree: a multiattribute indexing method with good guaranteed performance
ACM Transactions on Database Systems (TODS)
A general solution of the n-dimensional B-tree problem
SIGMOD '95 Proceedings of the 1995 ACM SIGMOD international conference on Management of data
The SR-tree: an index structure for high-dimensional nearest neighbor queries
SIGMOD '97 Proceedings of the 1997 ACM SIGMOD international conference on Management of data
On the analysis of indexing schemes
PODS '97 Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
A lower bound theorem for indexing schemes and its application to multidimensional range queries
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Tight bounds for 2-dimensional indexing schemes
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
The P-range tree: a new data structure for range searching in secondary memory
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Multidimensional binary search trees used for associative searching
Communications of the ACM
Design of Dynamic Data Structures
Design of Dynamic Data Structures
The K-D-B-tree: a search structure for large multidimensional dynamic indexes
SIGMOD '81 Proceedings of the 1981 ACM SIGMOD international conference on Management of data
R-trees: a dynamic index structure for spatial searching
SIGMOD '84 Proceedings of the 1984 ACM SIGMOD international conference on Management of data
Similarity Indexing with the SS-tree
ICDE '96 Proceedings of the Twelfth International Conference on Data Engineering
The X-tree: An Index Structure for High-Dimensional Data
VLDB '96 Proceedings of the 22th International Conference on Very Large Data Bases
Clustering Techniques for Minimizing External Path Length
VLDB '96 Proceedings of the 22th International Conference on Very Large Data Bases
Efficient Splitting and Merging Algorithms for Order Decomposable Problems (Extended Abstract)
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Online Data Structures in External Memory
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
Online Data Structures in External Memory
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
A Framework for Index Bulk Loading and Dynamization
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
External Memory Data Structures
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Query Responsive Index Structures
GIScience '08 Proceedings of the 5th international conference on Geographic Information Science
Recent Advances in Worst-Case Efficient Range Search Indexing
SSTD '09 Proceedings of the 11th International Symposium on Advances in Spatial and Temporal Databases
Untangled Monotonic Chains and Adaptive Range Search
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
External-memory algorithms and data structures
Algorithms and theory of computation handbook
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
Range queries over untangled chains
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Untangled monotonic chains and adaptive range search
Theoretical Computer Science
Indexability of 2D range search revisited: constant redundancy and weak indivisibility
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
I/O-efficient spatial data structures for range queries
SIGSPATIAL Special
SIGSPATIAL Special
Efficient processing of multiple continuous skyline queries over a data stream
Information Sciences: an International Journal
Efficient external memory structures for range-aggregate queries
Computational Geometry: Theory and Applications
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In this paper, we examine the complexity of multi-dimensional range searching in non-replicating index structures. Such nonreplicating structures achieve low storage costs and fast update times due to lack of multiple copies. We first obtain a lower bound for range searching in non-replicating structures. Assuming a simple tree structure model of an index, we prove that the worst-case time for a query retrieving t out of n data items is Ω((n/b)(d-1)/d + t/b), where d is the data dimensionality and b is the capacity of index nodes. We then propose a new index structure, called the O-tree, that achieves this query time in dynamic environments. Updates are supported in O(logb n) amortized time and exact match queries in O(logb n) worst-case time. This structure improves the query time of the best known non-replicating structure, the divided k-d tree, and is optimal for both queries and updates in non-replicating tree structures.