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The complexity of hashing with lazy deletion

Christopher J. Van Wyk, Jeffrey Scott Vitter
1986 Algorithmica  
We show that under several reasonable assumptions about the distribution of the items, hashing with lazy deletion uses little more space than methods that use eager deletion.  ...  delete an item; and 9 space complexity: the number of items stored by the data structure.  ...  Don also suggested looking at the stationary model. Thanks also to Brenda Baker, Brian Kernighan, Ian Munro, and an anonymous referee for helpful comments on the manuscript.  ... 
doi:10.1007/bf01840434 fatcat:p7eycszt6fghdefy5jnjq3wtze

A Queueing Analysis of Hashing with Lazy Deletion

John A. Morrison, Larry A. Shepp, Christopher J. Van Wyk
1987 SIAM journal on computing (Print)  
In this paper, we analyze the expected amount of excess space used by hashing with lazy deletion.  ...  On the other hand, its space overhead is much smaller than those more careful methods, so if the number of extra items is not too large, hashing with lazy deletion can be a practical algorithm when space  ...  Thanks to Jeff Vitter for several thoughtful comments on the manuscript.  ... 
doi:10.1137/0216073 fatcat:ye7fnqhk6jf57mkwx77uahr2hy

A New Dynamic Hash Index for Flash-Based Storage

Xiang Li, Zhou Da, Xiaofeng Meng
2008 2008 The Ninth International Conference on Web-Age Information Management  
The analysis and experimental results validate the efficiency of our design.  ...  In this paper we explore problems of indexing flash-resided data and present a new dynamical hash index for flash memory in two schemas.  ...  One is how to deal with the update/deletion of indexed data item. The other is how to dynamically manage the index structure itself.  ... 
doi:10.1109/waim.2008.53 dblp:conf/waim/LiDM08 fatcat:muf3lkhisbhtlk3o4u6ljbqwoi

On Deletions in Open Addressing Hashing [chapter]

Rosa M. Jiménez, Conrado Martínez
2018 2018 Proceedings of the Fifteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)  
In the second part we propose an algorithm for true deletion in open addressing hashing with secondary clustering, like quadratic hashing.  ...  In the first part of this paper we review a practical implementation of the often overlooked deletion algorithm for linear probing hash tables, analyze its properties and performance, and provide several  ...  Additionally, a precise mathematical analysis of the performance in the presence of insertions and lazy deletions is quite complex [3, 15] .  ... 
doi:10.1137/1.9781611975062.3 dblp:conf/analco/JimenezM18 fatcat:ozptpgqwlndfllpgohxmfu5zzi

CedrusDB: Persistent Key-Value Store with Memory-Mapped Lazy-Trie [article]

Maofan Yin, Hongbo Zhang, Robbert van Renesse, Emin Gün Sirer
2021 arXiv   pre-print
A "lazy-trie" is a variant of the hash-trie data structure that achieves near-optimal height, has practical storage overhead, and can be maintained on-disk with standard write-ahead logging.  ...  We implemented CedrusDB, persistent key-value store based on a lazy-trie. The lazy-trie is kept on disk while made available in memory using standard memory-mapping.  ...  The problem is that the lazy-trie must guarantee that keys with different hashes cannot be in the same linked list.  ... 
arXiv:2005.13762v3 fatcat:wkbsap2jbjf67eyesbc6zis4du

Efficient hash tables for network applications

Thomas Zink, Marcel Waldvogel
2015 SpringerPlus  
The introduction of hashing with multiple choices, d-left hashing and probabilistic table summaries, has caused a shift towards deterministic DRAM access.  ...  While in theory perfect hashing can provide optimal mapping, in practice, finding a perfect hash function is too expensive, especially in the context of high-speed applications.  ...  We use Eq. 8 for SF with lazy deletions, Eq. 9 for MBF with lazy deletions, Eq. 11 for counting SF, and Eq. 10 for counting MBF.  ... 
doi:10.1186/s40064-015-0958-y pmid:26020021 pmcid:PMC4441648 fatcat:g72wh7qnffc5jemtw4h72c3dhm

An index-split Bloom filter for deep packet inspection

Kun Huang, DaFang Zhang
2010 Science China Information Sciences  
Furthermore, we propose a lazy deletion algorithm and vacant insertion algorithm to reduce the update overhead of ISBF, where an on-chip deletion bitmap is used to update on-chip parallel CBFs, not adjusting  ...  Experimental results demonstrate that compared with the TriBiCa and SFHT, the ISBF significantly reduces the off-chip memory accesses and processing time of primitive operations, as well as both the on-chip  ...  Figure 4 describes the pseudo-codes of lazy deletion algorithm.  ... 
doi:10.1007/s11432-010-4132-4 fatcat:lr6znjfhjnd2fmb6p5kb6lo57q

NEFOS: Rapid Cache-Aware Range Query Processing with Probabilistic Guarantees [chapter]

Spyros Sioutas, Kostas Tsichlas, Ioannis Karydis, Yannis Manolopoulos, Yannis Theodoridis
2011 Lecture Notes in Computer Science  
The expected search bound holds with high probability for any (unknown) realistic input distribution.  ...  for the class of smooth only input distributions.  ...  The following theorem provides the complexities of the Lazy B-tree: Theorem 1.  ... 
doi:10.1007/978-3-642-23088-2_5 fatcat:2f6iiorwr5hs5mup5bmbjpx3oi

ISB-Tree: A New Indexing Scheme with Efficient Expected Behaviour [chapter]

Alexis Kaporis, Christos Makris, George Mavritsakis, Spyros Sioutas, Athanasios Tsakalidis, Kostas Tsichlas, Christos Zaroliagis
2005 Lecture Notes in Computer Science  
The expected search bound holds with high probability for a large class of (unknown) input distributions. The worst-case search bound of our indexing scheme is O (log B n) block transfers.  ...  in O (log B log n) expected block transfers, where B represents the disk block size and n denotes the number of stored elements.  ...  We are also indebted to the anonymous referees for their comments that improved the presentation of the paper.  ... 
doi:10.1007/11602613_33 fatcat:zse5yveecradpgk6k4g3e5ehcq

ISB-tree: A new indexing scheme with efficient expected behaviour

Alexis Kaporis, Christos Makris, George Mavritsakis, Spyros Sioutas, Athanasios Tsakalidis, Kostas Tsichlas, Christos Zaroliagis
2010 Journal of Discrete Algorithms  
The expected search bound holds with high probability for a large class of (unknown) input distributions. The worst-case search bound of our indexing scheme is O (log B n) block transfers.  ...  in O (log B log n) expected block transfers, where B represents the disk block size and n denotes the number of stored elements.  ...  We are also indebted to the anonymous referees for their comments that improved the presentation of the paper.  ... 
doi:10.1016/j.jda.2010.08.001 fatcat:77vb7b7ykjeobds7xadliwj5fi

Maximum Size of a Dynamic Data Structure: Hashing with Lazy Deletion Revisited

David Aldous, Micha Hofri, Wojciech Szpankowski
1992 SIAM journal on computing (Print)  
We study the dynamic data structure management technique called Hashing with Lazy Deletion (HwLD). A table managed under HwLD is built via. a sequence of insertions and deletions of items.  ...  When hashing with lazy deletions, one does not delete items as soon as possible, but keeps more items in the data structure than immediate-deletion strategies would.  ...  INTRODUCTION The purpose of this paper is to present a thorough analysis of Hashing with Lazy Deletion (HwLD) in a general probabilistic framework.  ... 
doi:10.1137/0221043 fatcat:f2gyckee5rcwvl5cvfsjfbfa5y

Distributed security storage model for large-scale data

Ming Zhang, Wei Chen, Yunpeng Cao
2017 Journal of Mathematics and Computer Science  
This security storage model can deal with the high concurrency and the complexity of large-scale data management in the distributed environment.  ...  With the development of large-scale data, the increasingly users need to store the data in the distributed storage system due to the fact that the signal computer can not hold the massive data.  ...  Finally the updated root hash is reencrypted with SL and stored in md-file. The time complexity is O(log(n)).  ... 
doi:10.22436/jmcs.017.04.05 fatcat:2p4kgu4larg3fborijtn4zgxba

The adaptive radix tree: ARTful indexing for main-memory databases

V. Leis, Alfons Kemper, T. Neumann
2013 2013 IEEE 29th International Conference on Data Engineering (ICDE)  
At the same time, ART is very space efficient and solves the problem of excessive worst-case space consumption, which plagues most radix trees, by adaptively choosing compact and efficient data structures  ...  Even though ART's performance is comparable to hash tables, it maintains the data in sorted order, which enables additional operations like range scan and prefix lookup.  ...  Fig. 15 . 15 Mix of lookups, insertions, and deletions (16M keys). Fig. 16 . 16 TPC-C performance. Fig. 17 . 17 Impact of lazy expansion and path compression on the height of the TPC-C indexes.  ... 
doi:10.1109/icde.2013.6544812 dblp:conf/icde/LeisK013 fatcat:sma67ydio5c5vpuok4axiruanu

Simple Summaries for Hashing With Choices

A. Kirsch, M. Mitzenmacher
2008 IEEE/ACM Transactions on Networking  
To address these issues, we explore two deletion paradigms: lazy deletions and counter-based deletion schemes. A. Lazy Deletions A natural, general approach is to use lazy deletions.  ...  The multiple filter scheme allows further space gains with just slightly more complexity.  ...  Theorem 1.1: Suppose we hash items into an MHT with tables (with corresponding fully random hash functions ), where the size of is for , for any constants and with .  ... 
doi:10.1109/tnet.2007.899058 fatcat:v7mw33h5wfhldkbgoy2o2bingy

Shed More Light on Bloom Filter's Variants [article]

Ripon Patgiri, Sabuzima Nayak, Samir Kumar Borgohain
2019 arXiv   pre-print
In this paper, we present a) in-depth insight on the Bloom Filter,and b) the prominent variants of the Bloom Filters.  ...  The Bloom Filter returns True Positive (TP), False Positive (FP), or True Negative (TN). The Bloom Filter is widely adapted in numerous areas to enhance the performance of a system.  ...  This Bloom Filter is a dictionary based and use the Backyard Cuckoo hashing [35] . To this hashing a similar lazy deletion method is applied as used by Thorup [36] .  ... 
arXiv:1903.12525v1 fatcat:vktcr3gmd5gkpjrwyvqmvjeye4
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