Binary Search Trees: Average and Worst Case Behavior (Extended Abstract)

Güttler, Reiner; Mehlhorn, Kurt; Schneider, Wolfgang; Wernet, Norbert

doi:10.1007/978-3-642-95289-0_22

Cited by 7 publications

(4 citation statements)

References 7 publications

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“…This observation is made precise in the following theorem. In the proof of Theorem 7.1, we use the following lemma, which follows from the results of [8].…”

Section: Computing Approximately Optimal Alphabetic Treesmentioning

confidence: 98%

A Parallel Algorithm for Optimum Height-Limited Alphabetic Binary Trees

Larmore

Przytycka²

1996

Journal of Parallel and Distributed Computing

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“…This observation is made precise in the following theorem. In the proof of Theorem 7.1, we use the following lemma, which follows from the results of [8].…”

Section: Computing Approximately Optimal Alphabetic Treesmentioning

confidence: 98%

A Parallel Algorithm for Optimum Height-Limited Alphabetic Binary Trees

Larmore

Przytycka²

1996

Journal of Parallel and Distributed Computing

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“…Our parallel algorithm utilizes the following approximating lemma due to Gu:ttler, Mehlhorn, and Schneider [7].…”

Section: Constructing Almost Optimal Binary Searching Trees In Parallelmentioning

confidence: 99%

“…given in the sense of Gu:ttler, Mehlhorn, and Schneider [7], of any optimal tree which has no subtrees (other than a single leaf) of weight less than 6.…”

Section: Let H = O(log(1/e)) Be the Maximum Heightmentioning

confidence: 99%

Constructing trees in parallel

Atallah

Kosaraju

Larmore

et al. 1989

Proceedings of the First Annual ACM Symposium on Parallel Algorithms and Architectures

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An O(log ~ n) time, n2/logn processor as well as an O(log n) time, n3/log n processor CREW deterministic parallel algorithms are presented for constructing Huffman codes from a given list of frequences. The time can be reduced to O(log n(loglog n) 2) on an CRCW model, using only n2/(log log n) 2 processors.Also presented is an optimal O(log n) time, O(n/log n) processor EREW parallel algorithm for constructing a tree given a list of leaf depths when the depths are monotonic. An O(log 2 n) time, n processor parallel algorithm is given for the general tree construction problem. We also give an O(log 2 n) time n2/log2n processor algorithm which finds a nearly optimal binary search tree. An O(log 2 n) time n 2'36 processor algorithm for recognizing linear context free languages is given. A crucial ingredient in achieving those bounds is a formulation of these problems as multiplications of special matrices which we call concave matrices. The structure of these matrices makes their parallel multiplication dramatically more efficient than that of arbitrary matrices.

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“…+ 2 j --j [2,12]. F u r t h e r m o r e these bounds are almost sharp for most nodes and leaves [5,17]. More precisely, for any d, I < d < ~ and h > o, let L h = 43; aj ~ ( l o g ( ] / a j ) -h ) / d~ a n d…”

mentioning

confidence: 99%