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An Improved Bound for Random Binary Search Trees with Concurrent Insertions

George Giakkoupis, Philipp Woelfel
unpublished
Whenever the buffer is full, or when all keys have arrived, an adversary chooses one key from the buffer and inserts it into the binary search tree.  ...  Recently, Aspnes and Ruppert (DISC 2016) defined the following simple random experiment to determine the impact of concurrency on the performance of binary search trees: n randomly permuted keys arrive  ...  An Improved Bound for Random Binary Search Trees with Concurrent Insertions We will now show for any i ∈ {0, . . . , n − 1} that |desc(i + 1)| ≤ δ c i − 2, and moreover, for a buffer of size c = 1, |desc  ... 
fatcat:yggwnag2hna73eoem4jmusz4ni

Page 6932 of Mathematical Reviews Vol. , Issue 93m [page]

1993 Mathematical Reviews  
Our improved bound immediately translates into improved CRCW-PRAM bounds for the numerous applications of this problem, including string edit- ing, construction of Huffman codes and other coding trees,  ...  An encoding of a binary tree is a function that assigns a unique label to a binary tree.  ... 

COMPUTER VISION: OBJECT TRACKING USING SELF-BALANCING TREE FOR OPTIMIZED DATA PROCESSING

Christopher Chan Vi, Shawn X. Wang, Christopher Ryu, Anand Panangadan
2021 Zenodo  
This research uses the AVL (Adelson-Velsky and Landis) self-balancing binary search tree to see differences in Asymptotic Runtime for insert and traversal operations.  ...  the AVL self-balancing Binary Search Tree can be used for optimization of data processing from a Computer Vision Robotics camera source?"  ...  AVL Self-Balancing Binary Search Tree AVL Self-Balancing Binary Search Trees have been around since 1962 and have seen a number of proposed improvements to them.  ... 
doi:10.5281/zenodo.5765022 fatcat:fiiqjdhht5bmpibgwpkrk4chny

Page 6315 of Mathematical Reviews Vol. , Issue 93k [page]

1993 Mathematical Reviews  
The analysis of the algorithm, by establishing an upper bound on the cost of the produced binary search trees, permits us to derive a bound on the cost of optimal binary search trees.  ...  Summary: “We present a new linear-time heuristic for constructing binary search trees.  ... 

HIGHER-ORDER ANALYSIS OF 2–3 TREES

RICARDO A. BAEZA-YATES, PATRICIO V. POBLETE
1995 International Journal of Foundations of Computer Science  
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 over ow techniques.  ...  We present a fourth-order fringe analysis for the expected behavior of 2-3 trees, which includes 97% of the elements in the tree.  ...  This should be compared with binary trees (with or without balance), where 33% of the space is used for keys.  ... 
doi:10.1142/s0129054195000020 fatcat:jhdhrn3bujg53ebduw3ua2ewru

Zip Trees [article]

Robert E. Tarjan, Caleb C. Levy, Stephen Timmel
2019 arXiv   pre-print
First, zip trees require only O(loglog n) bits (with high probability) to represent the largest rank in an n-node binary search tree; previous data structures require O(log n) bits for the largest rank  ...  A zip tree is a binary search tree in which each node has a numeric rank and the tree is (max)-heap-ordered with respect to ranks, with rank ties broken in favor of smaller keys.  ...  We thank Leon Sering for correcting the statement and proof of Lemma 2. Finally, we are grateful to Dominik Kempa for providing us with C++ zip-tree implementations, benchmarks, and general comments.  ... 
arXiv:1806.06726v4 fatcat:xbqoarqilzhafhiv6e2cen2yq4

A scalable sequence encoding for collaborative editing

Brice Nédelec, Pascal Molli, Achour Mostéfaoui
2017 Concurrency and Computation  
If the operations arrives to an editor out of order, the removal waits for the corresponding insertion. On the opposite, it immediately integrates received insertions.  ...  This causality tracking structure tracks only the semantically related pairs of operations (e.g. the removal of an element with its insertion).  ...  Repeated binary searches lead to the upper bound O( e i=1 (log 2 i )), where e is the depth of the tree.  ... 
doi:10.1002/cpe.4108 fatcat:ev63mcqgxrcd7ndj4gk7rq4jzi

DeltaTree: A Practical Locality-aware Concurrent Search Tree [article]

Ibrahim Umar, Otto Anshus, Phuong Ha
2013 arXiv   pre-print
the three concurrent search trees for searching operations and up to 1.6 times faster for update operations when the update contention is not too high.  ...  highly-concurrent search trees.  ...  The authors would like to thank Gerth Stølting Brodal for the source code used in [BFJ02] . Vincent Gramoli who provides the source code for Synchrobench from [CGR12] .  ... 
arXiv:1312.2628v1 fatcat:ys7o26dwmzbuviuq5z3j4gvvta

A Survey on Priority Queues [chapter]

Gerth Stølting Brodal
2013 Lecture Notes in Computer Science  
Back in 1964 Williams introduced the binary heap as a basic priority queue data structure supporting the operations Insert and Ex-tractMin in logarithmic time.  ...  Center for Massive Data Algorithms, a Center of the Danish National Research Foundation. 1 We let lg x denote the binary logarithm of x. 2 In the following we denote a data structure storing O(1) words  ...  Acknowledgment The author would like to thank Rolf Fagerberg, Andy Brodnik, Jyrki Katajainen, Amr Elmasry, Jesper Asbjørn Sindahl Nielsen and the anonymous reviewers for valuable input.  ... 
doi:10.1007/978-3-642-40273-9_11 fatcat:zocxhiyfmvdgzn2yoob25h3wr4

Rose

Russell Sears, Mark Callaghan, Eric Brewer
2008 Proceedings of the VLDB Endowment  
Rose avoids random I/O during replication and scans, leaving more I/O capacity for queries than existing systems, and providing scalable, real-time replication of seek-bound workloads.  ...  This allows Rose to provide atomicity, consistency and isolation to concurrent transactions without resorting to rollback, blocking index requests or interfering with maintenance tasks.  ...  ACKNOWLEDGEMENTS We would like to thank Petros Maniatis, Tyson Condie, Jens Dittrich and the anonymous reviewers for their feedback. Portions of this work were performed at Intel Research, Berkeley.  ... 
doi:10.14778/1453856.1453914 fatcat:phivdc64ifd2ngui7ptn6r4v2m

Fully dynamic distributed search trees can be balanced in time

Fabio Barillari, Enrico Nardelli, Massimo Pepe
2002 Journal of Parallel and Distributed Computing  
We prove that in the worst case a key can be inserted, searched, or deleted with Oðlg 2 NÞ messages. We show that for the introduced distributed search tree this bound is tight.  ...  We introduce a new version, based on AVL-trees, of distributed search trees, the first to be fully scalable, that is, able to both grow and shrink as long as keys are inserted and deleted.  ...  Many detailed and careful observations from one of them greatly helped in improving the quality of presentation.  ... 
doi:10.1016/s0743-7315(02)00009-6 fatcat:mfuizlyu65dfhfqs3nrzn4regu

The Power and Limitations of Static Binary Search Trees with Lazy Finger [article]

Prosenjit Bose and Karim Douïeb and John Iacono and Stefan Langerman
2013 arXiv   pre-print
A static binary search tree where every search starts from where the previous one ends (lazy finger) is considered.  ...  The runtime of the classic root-finger tree can be expressed in terms of the entropy of the distribution of the searches, but we show that this is not the case for the optimal lazy finger tree.  ...  Furthermore, Melhorn demonstrated a lower bound of 1 lg 3 H(f X ) for an average search in an optimal static tree, and showed this bound was tight for infinitely many distributions.  ... 
arXiv:1304.6897v1 fatcat:pnvqojayjzh3ljat3axgnlwebm

The Power and Limitations of Static Binary Search Trees with Lazy Finger

Prosenjit Bose, Karim Douïeb, John Iacono, Stefan Langerman
2016 Algorithmica  
A static binary search tree where every search starts from where the previous one ends (lazy finger ) is considered.  ...  The runtime of the classic root-finger tree can be expressed in terms of the entropy of the distribution of the searches, but we show that this is not the case for the optimal lazy finger tree.  ...  Furthermore, Melhorn demonstrated a lower bound of 1 lg 3 H(f X ) for an average search in an optimal static tree, and showed this bound was tight for infinitely many distributions.  ... 
doi:10.1007/s00453-016-0224-x fatcat:oksirg4s4fhsbl7euqemu3yp54

Page 510 of Mathematical Reviews Vol. , Issue 2002A [page]

2002 Mathematical Reviews  
The authors introduce a modification to the k-d tree (k- dimensional binary search tree). Their squarish k-d tree uses 68 COMPUTER SCIENCE 510 a different procedure for on-line insertion.  ...  Two operators, A and its dual A, are used, and two operations, a binary one, ©, for juxtaposition, and an n-ary one, |, for every n, for branching.  ... 

Efficient algorithms to globally balance a binary search tree

Hsi Chang, S. Sitharama Iyangar
1984 Communications of the ACM  
A binary search tree can be globally balanced by readjustment of pointers or with a sorting process in O(n) time, n being the total number of nodes.  ...  These algorithms show improvement in time efficiency over some sequential algorithms [1, 2, 7] when applied to large binary search trees. A comparison of various algorithms is presented.  ...  Acknowledgments The authors wish to thank an anonymous referee for a number of valuable suggestions and criticisms. Thanks are due to Professor Horowitz for his comments on our paper.  ... 
doi:10.1145/358105.358191 fatcat:onpod7q36jbkjobfkvjqyczxde
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