@article{Mehlhorn2005DynamicFC,
author={Kurt Mehlhorn and Stefan N{\"a}her},
journal={Algorithmica},
year={2005},
volume={5},
pages={215-241}
}
• Published 1 June 1990
• Computer Science
• Algorithmica
The problem of searching for a key in many ordered lists arises frequently in computational geometry. Chazelle and Guibas recently introduced fractional cascading as a general technique for solving this type of problem. In this paper we show that fractional cascading also supports insertions into and deletions from the lists efficiently. More specifically, we show that a search for a key inn lists takes timeO(logN +n log logN) and an insertion or deletion takes timeO(log logN). HereN is the…
112 Citations
A Lower Bound for Dynamic Fractional Cascading
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2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)
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This paper shows that it is actually possible to circumvent the lower bound of Chazelle and Liu for axis-aligned planar subdivisions for two-dimensional fractional cascading, and presents a number of upper and lower bounds which reveal that in two-dimensions, the problem has a much richer structure.
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It is shown that it is possible to circumvent the lower bound of Chazelle and Liu for axis-aligned planar subdivisions for fractional cascading, and a number of upper and lower bounds are presented which reveal that in 2D, the problem has a much richer structure.
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