@article{Aragon-1989,
author={C. R. Aragon and R. G. Seidel},
journal={30th Annual Symposium on Foundations of Computer Science},
title={Randomized search trees},
year={1989},
pages={540-545},
doi={10.1109/SFCS.1989.63531},
month={Oct},url = {http://faculty.washington.edu/aragon/pubs/rst89.pdf}}
@book{Grimmett-2001,
title = {Probability and Random Processes},
author = {Geoffrey R. Grimmett, David R. Stirzaker},
publisher = {Oxford University Press},
isbn = {9780198572237},
year = {2001},
series = {},
edition = {3rd},
volume = {},}
@article{Sleator-1988,
ISSN = {08940347, 10886834},
URL = {http://www.jstor.org/stable/1990951},
abstract = {A rotation in a binary tree is a local restructuring that changes the tree into another tree. Rotations are useful in the design of tree-based structures. The rotation distance between a pair of trees in the minimum number of rotations needed to convert one tree into the other. In this paper we establish a tight bound of 2n - 6 on the maximum rotation distance between two n-node trees for all large n. The hard and novel part of the proof is the lower bound, which makes use of volumetric arguments in hyperbolic 3-space. Our proof also gives a tight bound on the minimum number of tetrahedra needed to dissect a polyhedron in the worst case and reveals connections among binary trees, triangulations, polyhedra, and hyperbolic geometry.},
author = {Daniel D. Sleator and Robert E. Tarjan and William P. Thurston},
journal = {Journal of the American Mathematical Society},
number = {3},
pages = {647--681},
publisher = {American Mathematical Society},
title = {Rotation Distance, Triangulations, and Hyperbolic Geometry},
volume = {1},
year = {1988}
}
@article{Hoare-1962,
doi = {10.1093/comjnl/5.1.10},
title = {Quicksort},
author = {Hoare, C. A. R.},
publisher = {Oxford University Press},
journal = {The Computer Journal},
issnp = {0010-4620},
issne = {1460-2067},
year = {1962},
month = {Jan},
volume = {5},
issue = {1},
pages = {10--16},
url = {https://doi.org/10.1093/comjnl/5.1.10},
}
@article{Vuillemin-1980,
doi = {10.1145/358841.358852},
title = {A unifying look at data structures},
author = {Vuillemin, Jean},
publisher = {Association for Computing Machinery},
journal = {Communications of the ACM},
issnp = {0001-0782},
year = {1980},
month = {Apr},
volume = {23},
issue = {4},
pages = {229--239},
url = {https://pdfs.semanticscholar.org/1742/195ba5043ec45345d6a9c9ee65145d345ecd.pdf},
}
@Article{Sedgewick1977,
author="Sedgewick, Robert",
title="The analysis of Quicksort programs",
journal="Acta Informatica",
year="1977",
volume="7",
number="4",
pages="327--355",
abstract="The Quicksort sorting algorithm and its best variants are presented and analyzed. Results are derived which make it possible to obtain exact formulas describing the total expected running time of particular implementations on real computers of Quicksort and an improvement called the median-of-three modification. Detailed analysis of the effect of an implementation technique called loop unwrapping is presented. The paper is intended not only to present results of direct practical utility, but also to illustrate the intriguing mathematics which arises in the complete analysis of this important algorithm.",
issn="1432-0525",
doi="10.1007/BF00289467",
}
@article{Lagarias-2013,
doi = {10.1090/S0273-0979-2013-01423-X},
title = {Euler's constant: Euler's work and modern developments},
author = {Lagarias, Jeffrey C.},
publisher = {American Mathematical Society},
journal = {Bulletin of the American Mathematical Society},
issnp = {0273-0979},
issne = {1088-9485},
year = {2013},
month = {Jul},
volume = {50},
issue = {4},
page = {527--628},
url = {http://www.ams.org/journals/bull/2013-50-04/S0273-0979-2013-01423-X/S0273-0979-2013-01423-X.pdf},
}