Computational geometry: an introduction
Computational geometry: an introduction
The input/output complexity of sorting and related problems
Communications of the ACM
External-memory graph algorithms
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
I/O-complexity of graph algorithms
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Theory and practice of I/O-efficient algorithms for multidimensional batched searching problems
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
On showing lower bounds for external-memory computational geometry problems
External memory algorithms
The I/O - Complexity of Ordered Binary - Decision Diagram Manipulation
ISAAC '95 Proceedings of the 6th International Symposium on Algorithms and Computation
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
A General Lower Bound on the I/O-Complexity of Comparison-based Algorithms
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Algorithms and data structures for external memory
Foundations and Trends® in Theoretical Computer Science
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We propose a natural extension of algebraic decision trees to the external-memory setting, where the cost of disk operations overwhelms CPU time, and prove a tight lower bound of Ω(n logm n) on the complexity of both sorting and element uniqueness in this model of computation. We also prove a Ω(min{n logm n, N}) lower bound for both problems in a less restrictive model, which requires only that the worst-case internal-memory computation time is finite. Standard reductions immediately generalize these lower bounds to a large number of fundamental computational geometry problems.