Maintaining Ideally Distributed Random Search Trees without Extra Space

We consider the problem of maintaing a random binary search tree under insertions and deletions under the conditions that (i) no extra permanent storage space be used besides the tree itself, and (ii) that at any point in time the tree be perfectly random, meaning that it is drawn from the ideal binary search tree distribution. We present a simple solution to this problem with an expected deletion time of O(logn) and expected insertion time of O(log2 n) time.

[1]  Michaela Heyer,et al.  Randomness Preserving Deletions on Special Binary Search Trees , 2006, MFCSIT.

[2]  Donald E. Knuth,et al.  The Art of Computer Programming: Volume 3: Sorting and Searching , 1998 .

[3]  Kurt Mehlhorn,et al.  A Partial Analysis of Height-Balanced Trees Under Random Insertions and Deletions , 1982, SIAM J. Comput..

[4]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[5]  William Pugh,et al.  Skip lists: a probabilistic alternative to balanced trees , 1989, CACM.

[6]  Cecilia R. Aragon,et al.  Randomized search trees , 2005, Algorithmica.

[7]  Prof. Dr. Kurt Mehlhorn,et al.  Data Structures and Algorithms 3 , 2012, EATCS Monographs on Theoretical Computer Science.

[8]  Cecilia R. Aragon,et al.  Randomized search trees , 1989, 30th Annual Symposium on Foundations of Computer Science.

[9]  Conrado Martínez,et al.  Randomized binary search trees , 1998, JACM.

[10]  Jeffrey L Eppinger,et al.  An empirical study of insertion and deletion in binary search trees , 1983, Commun. ACM.

[11]  Donald E. Knuth,et al.  Deletions That Preserve Randomness , 1977, IEEE Transactions on Software Engineering.

[12]  Donald E. Knuth,et al.  A Trivial Algorithm Whose Analysis Isn't , 1978, J. Comput. Syst. Sci..