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Analysis of Hoare's FIND algorithm with Median-of-three partition

1997
*
Random structures & algorithms (Print)
*

*Hoare's*

*FIND*

*algorithm*can be used to select the jth element out

*of*a file

*of*n elements. ... In this paper, we consider the

*Median*-ofthree version, where the pivot element is chosen as the

*median*

*of*a random sample

*of*

*three*elements. ... The a¨erage number

*of*passes to select the j th element out

*of*a random permutation

*of*n elements using

*Hoare's*

*FIND*

*algorithm*

*with*

*Median*-

*of*-

*three*

*partition*is 24 18 18 12 12 P s H q H q H q ...

##
###
On Smoothed Analysis of Quicksort and Hoare's Find

2011
*
Algorithmica
*

We provide a smoothed

doi:10.1007/s00453-011-9490-9
fatcat:hxbm3ibofbah7lanvkbq65euui
*analysis**of**Hoare's**find**algorithm*and we revisit the smoothed*analysis**of*quicksort. ... Finally, we provide lower bounds for the smoothed number*of*comparisons*of*quicksort and*Hoare's**find*for the*median*-*of*-*three*pivot rule, which usually yields faster*algorithms*than always selecting the ... Scan Maxima*with**Median*-*of*-*three*Rule The results in this section serve as a basis for the*analysis**of*both quicksort and*Hoare's**find**with*the*median*-*of*-*three*rule. ...##
###
On Smoothed Analysis of Quicksort and Hoare's Find
[chapter]

2009
*
Lecture Notes in Computer Science
*

We provide a smoothed

doi:10.1007/978-3-642-02882-3_17
fatcat:2xkl2nkdyvaqnb6choq25cmeja
*analysis**of**Hoare's**find**algorithm*and we revisit the smoothed*analysis**of*quicksort. ... Finally, we provide lower bounds for the smoothed number*of*comparisons*of*quicksort and*Hoare's**find*for the*median*-*of*-*three*pivot rule, which usually yields faster*algorithms*than always selecting the ... Scan Maxima*with**Median*-*of*-*three*Rule The results in this section serve as a basis for the*analysis**of*both quicksort and*Hoare's**find**with*the*median*-*of*-*three*rule. ...##
###
Simple and Fast BlockQuicksort using Lomuto's Partitioning Scheme
[article]

2018
*
arXiv
*
pre-print

The simplification is achieved by using Lomuto's

arXiv:1810.12047v1
fatcat:ucoyedclabc2pgaxiigzeiyl3y
*partitioning*scheme instead*of**Hoare's*crossing pointer technique to*partition*the input. ... The paper provides an*analysis**of*the theoretical properties*of*the proposed*algorithms*and compares them to their competitors. ... Furthermore, we thank the anonymous reviewers for their suggestions that helped us in improving the presentation*of*this paper. ...##
###
Introspective Sorting and Selection Algorithms

1997
*
Software, Practice & Experience
*

A similar dilemma exists

doi:10.1002/(sici)1097-024x(199708)27:8<983::aid-spe117>3.0.co;2-#
fatcat:ry3jci2xfrfqbem5qbau7amxbu
*with*selection*algorithms*(for*finding*the i-th largest element) based on*partitioning*. ... For selection, a hybrid*of**Hoare's**FIND**algorithm*, which is linear on average but quadratic in the worst case, and the Blum-Floyd-Pratt-Rivest-Tarjan*algorithm*is as fast as*Hoare's**algorithm*in practice ... Stewart suggested the idea for the class*of*sequences K N . J. Valois and two anonymous referees made many useful comments on an earlier draft*of*this paper. ...##
###
Page 6546 of Mathematical Reviews Vol. , Issue 2000i
[page]

2000
*
Mathematical Reviews
*

*Hoare’s*classic recursive

*FIND*

*algorithm*[Comm. ACM 4 (1961), 321-322] to locate the /th smallest element

*of*a set S

*of*cardinality n, a random

*partitioning*element x is first chosen from the set S. ... {For the entire collection see MR 2000h:68007. } 20001:68036 68P10 68Q25 Griibel, Rudolf (D-HANN-IMS; Hannover) On the

*median*-

*of*-k version

*of*

*Hoare’s*selection

*algorithm*. (English summary) Theor. ...

##
###
Page 2049 of Mathematical Reviews Vol. , Issue 99c
[page]

1991
*
Mathematical Reviews
*

|Martinez, Conrado] (E-UPB-LI; Barcelona)

*Analysis**of**Hoare’s**FIND**algorithm**with**median*-*of*-*three**partition*. (English summary) Average-case*analysis**of**algorithms*(Dagstuhl, 1995). ... This article presents some results concerning the average number*of*passes and comparisons in*Hoare’s**Find**algorithm*in the case where the pivot element is the*median**of*a random sample*of**three*elements ...##
###
Page 7265 of Mathematical Reviews Vol. , Issue 98K
[page]

1998
*
Mathematical Reviews
*

Martinez [Conrado Martinez], Anal- ysis

*of**Hoare’s**FIND**algorithm**with**median*-*of*-*three**partition*(143-156); Guy Louchard, Probabilistic*analysis**of*adaptative sampling (157-168); Hosam M. ... {Some*of*the papers are being reviewed individually. } 98k:68003 68-06 68025 * Average-case*analysis**of**algorithms*. ...##
###
Theory and Implementation of Online Multiselection Algorithms
[chapter]

2013
*
Lecture Notes in Computer Science
*

We show that our online

doi:10.1007/978-3-642-40450-4_10
fatcat:wsib4ffh6jggfohha7gtqyccym
*algorithm*is 1-competitive in terms*of*data comparisons. ... We introduce a new online*algorithm*for the multiselection problem which performs a sequence*of*selection queries on a given unsorted array. ... Lemma 4 . 4 The number*of*comparisons required to*find*the*median**of**medians*and*partition*over all nodes v in the pivot tree T*with*at least 4 2 elements is within o(B(S t )) + O(n). ...##
###
On the median-of-k version of Hoare's selection algorithm

1999
*
RAIRO - Theoretical Informatics and Applications
*

A detailed

doi:10.1051/ita:1999112
fatcat:4b4nl452vffanbda3ewhgt6kgu
*analysis**of*the number*of*comparisons for k = 1 is given in Anderson and Brown [1] , who mention a renewed interest in*median*-*of*-*three*sélection. ... For the*median*-*of*-*three*version*of**FIND*we have the following explicit result. Theorem 3 . 3 mi(t) = 2 + 3t(l -t) for all t e [0,1]. ...##
###
BlockQuicksort: How Branch Mispredictions don't affect Quicksort
[article]

2016
*
arXiv
*
pre-print

elements); then, all elements in one block are compared

arXiv:1604.06697v2
fatcat:3xg63b7jqbfetcotcf6ws5xsfe
*with*the pivot and the outcomes*of*the comparisons are stored in a buffer. ... Since the work*of*Kaligosi and Sanders (2006), it is well-known that Quicksort -- which is commonly considered as one*of*the fastest in-place sorting*algorithms*-- suffers in an essential way from branch ... We are also indebted to Jan Philipp Wächter for all his help*with*creating the plots, to Daniel Bahrdt for answering many C++ questions, and to Christoph Greulich for his help*with*the experiments. ...##
###
A two-pass exact algorithm for selection on Parallel Disk Systems

2013
*
2013 IEEE Symposium on Computers and Communications (ISCC)
*

Our

doi:10.1109/iscc.2013.6755015
pmid:25374478
pmcid:PMC4217089
dblp:conf/iscc/MiR13
fatcat:zxxoauobrndhpbcb5lm6jt5y7a
*analysis*shows that DSS is a (2 + ε)-pass*algorithm*when the total number*of*input elements N is a polynomial in the memory size M (i.e., N = M c for some constant c). ... Numerous OLAP queries process selection operations*of*"top N",*median*, "top 5%", in data warehousing applications. ... The selection problem is to identify the i th smallest element from out*of*N given input elements. In particular,*finding*the*median*has various applications in data*analysis*. ...##
###
Analysis of Quickselect Under Yaroslavskiy's Dual-Pivoting Algorithm

2014
*
Algorithmica
*

We investigate the number

doi:10.1007/s00453-014-9953-x
fatcat:56nj7h2bkfcmdeygozivnmdil4
*of*comparisons made by Quickselect to*find*a key*with*a randomly selected rank under Yaroslavskiy's*algorithm*. ... There is excitement within the*algorithms*community about a new*partitioning*method introduced by Yaroslavskiy. ... The one-sided version (Quickselect)*of*the*algorithm*can be used to*find*order statistics. It is also known as*Hoare's*"*Find*"*algorithm*, which was first given in [15] . ...##
###
Fast Multidimensional Entropy Estimation by $k$-d Partitioning

2009
*
IEEE Signal Processing Letters
*

The estimator uses an adaptive

doi:10.1109/lsp.2009.2017346
fatcat:ubylrtowtzgkhahsgdn4d5bdvy
*partitioning*method and runs in Θ N log N time,*with*low memory requirements. ... We describe a non-parametric estimator for the differential entropy*of*a multidimensional distribution, given a limited set*of*data points, by a recursive rectilinear*partitioning*. ... For our*algorithm*, the time complexity is dominated by the*median**partitioning*, which we perform in Θ N time using*Hoare's*method [22] . ...##
###
Knowledge-based clustering of ship trajectories using density-based approach

2014
*
2014 IEEE International Conference on Big Data (Big Data)
*

While there is a large amount

doi:10.1109/bigdata.2014.7004281
dblp:conf/bigdataconf/LiuSMS14
fatcat:obaimaagjfcybfbwlyvoiglatu
*of*data*with*variable quality, decision makers need reliable information about possible situations or threats. ... The main result*of*clustering is a set*of*generated lanes that can be mapped to those defined in the IMO directives. ... ACKNOWLEDGMENT The authors acknowledge the generous support*of*GSTS, Inc., ExactEarth, Inc. and the Natural Science and Engineering Research Council*of*Canada for this research. ...
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