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Counting Inversions in Lists

Anupam Gupta, Francis X. Zane
2018
In a recent paper, Ajtai et al. [1] give a streaming algorithm to count the number of inversions in a stream Lε[m]n using two passes and O(ε−1-√n log n(log m + log n)) space.  ...  Our algorithm is based on estimating quantiles of the items already seen in the stream, and using that to estimate the number of inversions involving each element.  ...  In order to simplify our notation, we restate this in an equivalent form, that of counting non-inversions in the list when the total order, and thus the results of all strict comparisons, has been reversed  ... 
doi:10.1184/r1/6604550 fatcat:txnzfn6wvrhbjl7g5ihhtekgve

Counting Inversions Adaptively [article]

Amr Elmasry
2015 arXiv   pre-print
We give a simple and efficient algorithm for adaptively counting inversions in a sequence of n integers.  ...  Our algorithm runs in O(n + n √((Inv/n))) time in the word-RAM model of computation, where Inv is the number of inversions.  ...  While passing by the header of a list, the count of its elements is added to the inversions count.  ... 
arXiv:1503.01192v1 fatcat:url3d2uwyvcojcqg2lysmbna4u

Clustering mass spectrometry data using order statistics

Douglas J. Slotta, Lenwood S. Heath, Naren Ramakrishnan, Rich Helm, Malcolm Potts
2003 Proteomics  
Order statistics are used to provide a distance metric between each ordered list of peak heights from the samples.  ...  By comparing the resulting inversion count to the expected inversion count of a random ordering of the same list, the likelihood of correspondence can be computed [2] .  ...  The possible inversion counts for all permutations of a list follow a normal distribution [1] .  ... 
doi:10.1002/pmic.200300517 pmid:12973726 fatcat:ny7wgd7xerdeng4k4zdmcgbpmy

A simple shuffle-based stable in-place merge algorithm

Mehmet Emin Dalkilic, Elif Acar, Gorkem Tokatli
2011 Procedia Computer Science  
Sorting is one of the most fundamental problems in computer science.  ...  Then, using the knowledge that odd and evenindexed numbers are sorted among themselves, comparisons are made and then misplaced elements are relocated by applying successive inverse perfect shuffle and  ...  Otherwise, we should perform Inverse-shuffle algorithm to interval starting from curi, up to the end of the list. After the Inverse-shuffle, the element in curi is placed on its correct location.  ... 
doi:10.1016/j.procs.2010.12.172 fatcat:y5uneohrt5dhledaiw7szxinxm

Do senior CS students capitalize on recursion?

David Ginat
2004 Proceedings of the 9th annual SIGCSE conference on Innovation and technology in computer science education - ITiCSE '04  
CS students learn and practice recursion in CS1, Data-Structures, Introduction-to-Algorithms, and additional courses throughout the curriculum.  ...  involved counting of the number of inversions in a list of numbers.  ...  ) } The two recursive calls Inversions(left_L) and Inversions(right_L) return left_L and right_L as ordered lists, together with the number of inversions in each of these lists.  ... 
doi:10.1145/1007996.1008020 dblp:conf/iticse/Ginat04a fatcat:kg3jyi33njgz3p64s6kreee5pm

Do senior CS students capitalize on recursion?

David Ginat
2004 ACM SIGCSE Bulletin  
CS students learn and practice recursion in CS1, Data-Structures, Introduction-to-Algorithms, and additional courses throughout the curriculum.  ...  involved counting of the number of inversions in a list of numbers.  ...  ) } The two recursive calls Inversions(left_L) and Inversions(right_L) return left_L and right_L as ordered lists, together with the number of inversions in each of these lists.  ... 
doi:10.1145/1026487.1008020 fatcat:qzecywow7zdwfeswys76srx6oq

New Results for Adaptive and Approximate Counting of Inversions [article]

Saladi Rahul
2016 arXiv   pre-print
Counting inversions is a classic and important problem in databases. The number of inversions, K^*, in a list L=(L(1),L(2),...,L(n)) is defined as the number of pairs i < j with L(i) > L(j).  ...  In this paper, we handle a general case where each L(i) is a real number.  ...  INTRODUCTION In this paper we revisit the classic database problem of counting inversions.  ... 
arXiv:1612.08097v1 fatcat:qbpky6gdhrarfoysu6vi3lki74

An experiment of the complexity of sliding block puzzles by 2D heat flow in paramodulation [article]

Ruo Ando, Yoshiyasu Takefuji
2022 arXiv   pre-print
In the experiment, we have generated 500 * 8 puzzles under the test of the solvability checking by counting inversions.  ...  In this paper, we present a curious experiment with the hot list strategy in solving sliding block puzzles by paramodulation.  ...  At lines 2 to 9, the number of inversions of each slot is counted. These figures are counted up at lines 11 to 14. Finally, the sum is checked if it is an even or odd number at lines 15 to 19. VI.  ... 
arXiv:2201.03301v1 fatcat:jgxvsbb6dbakrm6xafhw6zvjiu

Listing Words in Free Groups [article]

Colin Ramsay
2017 arXiv   pre-print
In combinatorial group theory elements of a group are typically written as words in the generators and their inverses, and necklaces and bracelets correspond to conjugacy classes and relators respectively  ...  We present algorithms to generate lists of freely and cyclically reduced necklaces and bracelets in free groups.  ...  So, in the context of F g , listing the reduced bracelets of length is equivalent to listing equivalence classes of possible relators of length in a presentation.  ... 
arXiv:1706.08188v1 fatcat:6edg6fweuvhk3b3qhy72v7dr5e

A Cost Minimization Approach to Synthesis of Linear Reversible Circuits [article]

Ben Schaeffer, Marek Perkowski
2014 arXiv   pre-print
Results show that of the three methods MCG had the lowest average CNOT gate counts for linear reversible circuits up to 24 lines, and that AECM had the lowest counts between 28 and 60 lines.  ...  The last operation in the MCG algorithm transfers CNOT gates in the output-side CNOT gate list to the input-side CNOT gate list.  ...  In these cases the CNOT gate list can be rearranged to detect pairs of identical CNOT gates. Because CNOT gates are self-inverse [2] , all detected identical CNOT gate pairs can be erased.  ... 
arXiv:1407.0070v1 fatcat:go2nzidnnfbifiobkvyhkpbrpq

Requirement Tracing using Term Extraction [article]

Najla Al-Saati, Raghda Abdul-Jaleel
2015 arXiv   pre-print
Requirements traceability is an essential step in ensuring the quality of software during the early stages of its development life cycle.  ...  Having two candidate link list, say list X and list Y, with the same recall and precision, in that case if the true links show up at the top of list X compared with list Y, then obviously list X have preference  ...  Assuming Tj to be the total term count in document j, w i is calculated as in Eq.  ... 
arXiv:1506.08789v1 fatcat:w6v5zhp5ynalzjtw7izcu3a7my

Page 496 of Psychological Abstracts Vol. 42, Issue 4 [page]

1968 Psychological Abstracts  
with inversions that left phrase boundaries intact, and, for structurally equivalent types of inversion, the earlier in the string the inversion occurred the longer was the identification ume.  ...  —In a group testing procedure, 480 Ss were given a single trial to learn a list of 5 nonsense syllables, presented | at a time in order.  ... 

The Authors' Reply

J. David Bessman, Larry J. Williams, James Hokanson, P. R. Gilmer
1984 American Journal of Clinical Pathology  
) and platelet count.  ...  and associates demonstrated with an electronic impedance instrument (Coulter Counter model S-Plus®) that in 683 normal subjects there was a nonlinear, inverse relation between mean platelet volume (MPV  ...  The inverse relation between platelet size and count in normal subjects, and an artifact of other particles.  ... 
doi:10.1093/ajcp/81.3.406a fatcat:us6ffea56jcmbozm644sog2gca

Amortized efficiency of list update and paging rules

Daniel D. Sleator, Robert E. Tarjan
1985 Communications of the ACM  
In this article we study the amortized efficiency of the "move-to-front" and similar rules for dynamically maintaining a linear list.  ...  Other natural heuristics, such as the transpose and frequency count rules, da not share this property.  ...  Then the number of items preceding i in both lists is k -1 -xi. Moving i to the front of MF's list creates k -1 -Xi inversions and destroys x8 other inversions.  ... 
doi:10.1145/2786.2793 fatcat:lpj2jwspazgy3kgcyar5lotnnu

Algorithm Visualization [chapter]

2005 Computer Science Education Research  
The Examples drop-down list provides the user with example inputs to select and use, as shown in Figure 6.6 for the Counting Inversions AV.  ...  I used D3 to draw and manipulate the array in the Counting Inversions AV.  ... 
doi:10.1201/9781482287325-23 fatcat:oaz2w5lhmrhbdn7jaanwvfjjjq
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