Higher-Order Analysis of 2-3 Trees

@article{BaezaYates1995HigherOrderAO,
  title={Higher-Order Analysis of 2-3 Trees},
  author={Ricardo Baeza-Yates and Patricio V. Poblete},
  journal={Int. J. Found. Comput. Sci.},
  year={1995},
  volume={6},
  pages={1-10}
}
We present a fourth-order fringe analysis for the expected behavior of 2–3 trees, which includes 97% of the elements in the tree. It is accomplished by exploiting the structure of the transition matrix. Our results improve a number of bounds, in particular the bounds on the expected number of nodes and the expected space utilization. We also study 2–3 trees built by using overflow techniques. 
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References

SHOWING 1-10 OF 11 REFERENCES
Fringe analysis revisited
TLDR
The main results regarding fringe analysis are surveyed, a previous asymptotic theorem is improved, and new developments and applications of the theory are presented that allow improvements in several bounds on the behavior of search trees.
Some Observations on Random 2-3 Trees
Two Applications of Urn Processes The Fringe Analysis of Search Trees and The Simulation of Quasi-Stationary Distributions of Markov Chains
From an urn containing colored balls, one ball is drawn and replaced by a random number of differently colored balls, with the distribution of the added balls depending only on the color of the ball
Approaches to Concurrency in B-Trees
TLDR
The solut ions avai lable at the present time are surveyed, two main types of solut ion are proposed, which categorize almost a l l Solut ions in the l i t e r a t u r e .
Handbook of algorithms and data structures: in Pascal and C (2nd ed.)
TLDR
This chapter discusses algorithms in the context of graph programming, and some examples of algorithms used in the programming languages such as Python and Ruby are discussed.
An asymptotic analysis of minimum order B-trees
  • Dept. of Computing and Information Sciences
  • 1976
Reduction of the transition matrix of a fringe analysis and its application to the analysis of 2-3 trees
  • 5th International Conference of the Chilean Computer Science Society
  • 1985
On random 3-2 trees
  • On random 3-2 trees
  • 1974
...
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