### Randomized binary search treesRandomized binary search trees

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 Author Martnez, Conrado ♦ Roura, Salvador Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1998 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Balanced trees ♦ Probabilistic algebraic specification ♦ Randomized data structures ♦ Search trees ♦ Self-organizing data structures Abstract In this paper, we present randomized algorithms over binary search trees such that: (a) the insertion of a set of keys, in any fixed order, into an initially empty tree always produces a random binary search tree; (b) the deletion of any key from a random binary search tree results in a random binary search tree; (c) the random choices made by the algorithms are based upon the sizes of the subtrees of the tree; this implies that we can support accesses by rank without additional storage requirements or modification of the data structures; and (d) the cost of any elementary operation, measured as the number of visited nodes, is the same as the expected cost of its standard deterministic counterpart; hence, all search and update operations have guaranteed expected cost O(log $\textit{n}),$ but now irrespective of any assumption on the input distribution. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1998-03-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 45 Issue Number 2 Page Count 36 Starting Page 288 Ending Page 323

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Source: ACM Digital Library