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Balance in AVL trees and space cost of brother trees

Helen Cameron, Derick Wood
<span title="">1994</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
Abstraci Cameron, H. and D. Wood, Balance in AVL trees and space cost of brother trees, Theoretical Computer Science 127 (1994) 199-228.  ...  We obtain the result from a characterization of brother trees with the maximum space costs for their heights and weights.  ...  In Section 2, we define brother trees, the detailed profile of a brother tree, and the space cost of a brother tree.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(94)90040-x">doi:10.1016/0304-3975(94)90040-x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/f6vczb76cvesxihma3els6fy7q">fatcat:f6vczb76cvesxihma3els6fy7q</a> </span>
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Page 5001 of Mathematical Reviews Vol. , Issue 96h [page]

<span title="">1996</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
(3-WON-C; London, ON) Balance in AVL trees and space cost of brother trees.  ...  The major result of this paper is the characteri- zation of a family of locally space-cost pessimal (SCP) brother trees, i.e. brother trees with maximum space cost for given height and size.  ... 
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A tight upper bound for the path length of AVL trees

Rolf Klein, Derick Wood
<span title="">1990</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
These results carry over to the comparison cost of brother trees.  ...  Almost 25 years ago, Adel'son-Vel'skii and Landis [ 11 introduced AVL trees, the first class of which came to be known as balanced trees.  ...  binary and The space cost SCOST of a rother tree is the number of internal binary and unary nodes.  ... 
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A dichromatic framework for balanced trees

Leo J. Guibas, Robert Sedgewick
<span title="">1978</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/v4uclqixrrhlnk5pbw4wii6cfq" style="color: black;">19th Annual Symposium on Foundations of Computer Science (sfcs 1978)</a> </i> &nbsp;
ABSTUACT I() this paper we present a uniform framework for the implementation and study of halanced tree algorithms.  ...  \Ve show how to imhcd in this framework the best known halanced tree tecilIliques and thell usc the framework to deVl'lop new al1~orithJlls which perform the update and rebalancing in one pass, Oil the  ...  AVL trees (new initialization and balancing loop for Program 1). subtree below has increased in height by 1 (from even to odd) and that the height of its brother is equal or one less.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/sfcs.1978.3">doi:10.1109/sfcs.1978.3</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/focs/GuibasS78.html">dblp:conf/focs/GuibasS78</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/afeazmj4svdslbzfgaykol3nnq">fatcat:afeazmj4svdslbzfgaykol3nnq</a> </span>
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Page 2802 of Mathematical Reviews Vol. , Issue 81G [page]

<span title="">1981</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
.; Wood, D. 1-2 brother trees or AVL trees revisited. Comput. J. 23 (1980), no. 3, 248-255.  ...  Secondly, it is proved that the space utilisation of (random) 1-2 brother trees is much better than that for (random) 2-3 trees.  ... 
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Author Index Volume 127 (1994)

<span title="">1994</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
Wood, Balance in AVL trees and space cost of brother trees (Fundamenfal Study) Codenotti, B., M. Leoncini and G. Resta, Oracle computations in parallel numerical linear algebra Coquide, J.-L., M.  ...  ( The issue number is given in front of the page numbers) Barcucci, E., R. Pinzani and R. Sprugnoli, The random generation of directed animals Cameron, H. and D.  ... 
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The node visit cost of brother trees

Rolf Klein, Derick Wood
<span title="">1987</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/joe2ngto45hbnl3pncnesnq344" style="color: black;">Information and Computation</a> </i> &nbsp;
The performance of a brother search tree depends on its shape; it can be measured by three basic cost measures: node visit cost, comparison cost, and space cost.  ...  The structure of brother trees that are optimal with respect to each of these cost measures is already known, as well as how to construct them in linear time.  ...  ACKNOWLEDGMENTS The first author thanks his wife Anne Briiggemann-Klein for introducing him to T,X and for T,Xnical help. RECEIVED July 7, 1986; ACCEPTED April 10, 1987  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0890-5401(87)90053-8">doi:10.1016/0890-5401(87)90053-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/trh54bpjxfarppxgdie6ffaxfi">fatcat:trh54bpjxfarppxgdie6ffaxfi</a> </span>
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B-trees with lazy parent split

Yannis Manolopoulos
<span title="">1994</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ozlq63ehnjeqxf6cuxxn27cqra" style="color: black;">Information Sciences</a> </i> &nbsp;
Time and space performance results are also reported and comparison with conventional B-trees is carried out.  ...  A B-tree variant that postpones parent node splittings due to upcoming items until a later access of the same node is examined.  ...  This problem has been studied in depth, not only with respect to the family of B-trees, but also for binary search trees, AVL trees, linear hashing, etc.  ... 
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Dynamic load balancing algorithm for large data flow in distributed complex networks

Zhuo Zhang
<span title="2018-11-23">2018</span> <i title="Walter de Gruyter GmbH"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/r4ecuox7yrdy7h75vf7dx5nbau" style="color: black;">Open Physics</a> </i> &nbsp;
By introducing the relationship between nodes and the children of their brother nodes, we reduce the height of the whole sorted binary tree.  ...  This paper studies the commonly used NoSQL database and load balancing algorithms, and designs and implements a more efficient load balancing algorithm.  ...  It is only slightly higher than the AVL tree in the number of times of rotation, and the overall e ciency is very high. The e ect is satisfactory. .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1515/phys-2018-0089">doi:10.1515/phys-2018-0089</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uze6lojkbfdxdj7hr3wolmyy5e">fatcat:uze6lojkbfdxdj7hr3wolmyy5e</a> </span>
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An application of $m$-ary trees to the design of data structures for geometric searching problems

M. Talamo, G. Gambosi
<span title="">1989</span> <i title="EDP Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/foywj2stzfcwdln5izx2cxkroe" style="color: black;">RAIRO - Theoretical Informatics and Applications</a> </i> &nbsp;
Such dictionaries can be implemented by e. g. balanced trees (AVL trees, 2-3 trees, etc).  ...  balancée 6-ary tree, Q (n) = O (\g b n + lgn + fc) with fc the number of points resulting from the query: this gives a bound O (lg n 4-fe).  ... 
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Purely Functional Worst Case Constant Time Catenable Sorted Lists [chapter]

Gerth Stølting Brodal, Christos Makris, Kostas Tsichlas
<span title="">2006</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We present a purely functional implementation of search trees that requires O(log n) time for search and update operations and supports the join of two trees in worst case constant time.  ...  Hence, we solve an open problem posed by Kaplan and Tarjan as to whether it is possible to envisage a data structure supporting simultaneously the join operation in O(1) time and the search and update  ...  It seems quite hard to do this in the proposed structure because of the dependence of Property 2 on the rank of the tree.  ... 
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<a target="_blank" rel="noopener" href="https://web.archive.org/web/20160909091309/http://www.cs.au.dk:80/~gerth/papers/esa06trees.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/55/ef/55ef89745baf317abbfb6b21ab8753207fa405a4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11841036_18"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Adaptive structuring of binary search trees using conditional rotations

R.P. Cheetham, B.J. Oommen, D.T.H. Ng
<span title="">1993</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ht3yl6qfebhwrg7vrxkz4gxv3q" style="color: black;">IEEE Transactions on Knowledge and Data Engineering</a> </i> &nbsp;
In this scheme the restructuring is performed only if it decreases the Weighted Path Length (WPL) of the overall resultant tree.  ...  ,s N ] and are to be arranged lexicographically using a Binary Search Tree (BST). If S is known a priori, it is well known [10] that an optimal BST may be constructed using A and S.  ...  If the tree is reckoned to be "unbalanced", just as in the case of the AVL-tree [10] , the BB[α]-tree reorganizes the nodes using single or double rotations.  ... 
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<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170706035631/http://people.scs.carleton.ca:8008/%7Eoommen/papers/ConRotSm.PDF" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/2b/f9/2bf9e272c8acbf006791384796e03079878cf74e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/69.234780"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Identifying Occurrences of Maximal Pairs in Multiple Strings [chapter]

Costas S. Iliopoulos, Christos Makris, Spiros Sioutas, Athanasios Tsakalidis, Kostas Tsichlas
<span title="">2002</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
A molecular sequence "model" is a (structured) sequence of distinct or identical strings separated by gaps; here we design and analyze efficient algorithms for variations of the "Model Matching" and "Model  ...  Lemma 2 2 Two height-balanced trees of size n and m, where n ≤ m, can be merged in time O(log n+m n ).  ...  First, the following lemma on the merge operation of two height-balanced trees from [3] must be given. Proof. Assume two height-balanced trees T and T ′ of size n and m respectively, where n ≤ m.  ... 
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Master index volumes 121–130

<span title="">1994</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
Baccelli 125(1) Cameron, H. and D. Wood, Balance in AVL trees and space cost of brother trees (Fundamental Study) Chaunier, C. and N.  ...  Cocco and M. Fabris, Norms on terms and their use in proving universal termination of a logic program 124 (2) (1994) 297-328 Bouchitte, V., see M.R.  ...  and supersequence problems 125 (2)  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(94)90224-0">doi:10.1016/0304-3975(94)90224-0</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ottl7alcxjeknjceiiu4izki3m">fatcat:ottl7alcxjeknjceiiu4izki3m</a> </span>
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Pattern matching in Lempel-Ziv compressed strings: fast, simple, and deterministic [article]

Pawel Gawrychowski
<span title="2011-04-21">2011</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
representation of a string t[1..N], does s occur in t?  ...  We improve their result by developing a faster and fully deterministic O(nlog(N/n)+m) time algorithm with the same space complexity.  ...  The space usage of the improved algorithm is the same as in the solution of Farach and Thorup, O(n log N n + m).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1104.4203v1">arXiv:1104.4203v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/szdm2ymgg5boddghl74d5xoj6q">fatcat:szdm2ymgg5boddghl74d5xoj6q</a> </span>
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