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An in-place sorting with O(nlog n) comparisons and O(n) moves

Gianni Franceschini, Viliam Geffert
2005 Journal of the ACM  
We present the first in-place algorithm for sorting an array of size n that performs, in the worst case, at most O(n log n) element comparisons and O(n) element transports.  ...  This solves a long-standing open problem, stated explicitly, for example, in Munro and Raman [1992], of whether there exists a sorting algorithm that matches the asymptotic lower bounds on all computational  ...  The corresponding heap tree is thus of constant height, which results in an algorithm sorting with O(n) moves, O(1) storage, and O(n 1+ε ) comparisons.  ... 
doi:10.1145/1082036.1082037 fatcat:n36ky7vl6jfsdacyh3zc6dmcma

An In-Place Sorting with O(n log n) Comparisons and O(n) Moves [article]

Gianni Franceschini, Viliam Geffert
2003 arXiv   pre-print
We present the first in-place algorithm for sorting an array of size n that performs, in the worst case, at most O(n log n) element comparisons and O(n) element transports.  ...  ., in [J.I. Munro and V. Raman, Sorting with minimum data movement, J.  ...  Our algorithm operates in-place, with at most 2n·log n + o(n·log n) element comparisons and (13+ε)·n element moves in the worst case, for each n ≥ 1.  ... 
arXiv:cs/0305005v1 fatcat:zc5qqdgpyre4bohnzxjlb4xqqi

A deciding algorithm for linear isomorphism of types with complexity O(nlog 2(n)) [chapter]

A. Andreev, S. Soloviev
1997 Lecture Notes in Computer Science  
We describe an algorithm deciding if two types are linearly isomorphic with complexity O(nlog 2 (n)).  ...  It is known, that ordinary isomorphisms (associativity and commutativity of \times", isomorphisms for \times" unit and currying) provide a complete axiomatisation of isomorphism of types in multiplicative  ...  Acknowledgements We would like to thank Michael Rittri and Roberto Di Cosmo for many stimulating discussions of the matter, and Glynn Winskel and U e Engberg for helpful attention to our work while at  ... 
doi:10.1007/bfb0026989 fatcat:rooxkruyfbdariuve5xkjhoyme

Algorithms for Moving Objects Databases

J. A. Cotelo Lema
2003 Computer journal  
In earlier work we have proposed an approach based on abstract data types. Hence, moving point or moving region are viewed as data types with suitable operations.  ...  Algorithms are meant to be used in a database context; we also address filtering techniques and practical issues such as large object management or numeric robustness in the context of an ongoing prototype  ...  In any case the size of a is O(M). For the second argument b and for the result of an operation, we use with the same meaning N and R, respectively.  ... 
doi:10.1093/comjnl/46.6.680 fatcat:qjxmhcvmcncd7pnzu6n7j4sfuq

Sorting Short Keys in Circuits of Size o(n log n) [article]

Gilad Asharov, Wei-Kai Lin, Elaine Shi
2020 arXiv   pre-print
We consider the classical problem of sorting an input array containing n elements, where each element is described with a k-bit comparison-key and a w-bit payload.  ...  Specifically, we prove that there is a circuit with (k + w) · O(n k) ·(log^*n - log^* (w + k)) boolean gates capable of sorting any input array containing n elements, each described with a k-bit key and  ...  This work is in part supported by an NSF CAREER Award under the award number CNS-1601879, a Packard Fellowship, an ONR YIP award, and a DARPA Brandeis award.  ... 
arXiv:2010.09884v2 fatcat:ji2762hgevbpxijglqczbp5sxu

Matrix Sort - A Parallelizable Sorting Algorithm

S. Kavitha, Vijay V., Saketh A.
2016 International Journal of Computer Applications  
It has a time complexity of O(nnlogn) and hence takes lesser time than existing O(n 2 ) algorithms.  ...  In this paper, a new sorting algorithm called Matrix sort is introduced. This algorithm aims to sort the elements of a matrix without disturbing the matrix structure.  ...  Consider such an input matrix with n elements organized inn rows andn columns. For such an input, the top-down operation ends only in the √ n th iteration, for an input matrix with n elements.  ... 
doi:10.5120/ijca2016910341 fatcat:bin4yjmxyzaivm2zbeecvvkf4a

Heap Sorting Based on Array Sorting

Haiming Li, Ping Chen, Yong Wang
2017 Journal of Computer and Communications  
A kind of heap sorting method based on array sorting was proposed. Some advantages and disadvantages of it were discussed. It was compared with the traditional method of direct application.  ...  In the method, the ordered keywords in the array are put into the heap one by one after building an empty heap. This method needs relatively less space and is fit for ordered sequence.  ...  The lower bound of time complexity is O(nlog(2,n) and the worst case is O(n^2).  ... 
doi:10.4236/jcc.2017.512006 fatcat:7cpqc5iyxbapzdypoh7pi2x4cy

Multiway In-Place Merging [chapter]

Viliam Geffert, Jozef Gajdoš
2009 Lecture Notes in Computer Science  
Then, for s = n 2/3 /(log n) 1/3 , this gives an algorithm performing Θ(log k ·n) + O((n·log n) 2/3 ) comparisons andn + O((n·log n) 2/3 ) moves.  ...  That is, our algorithm runs in linear time, with an asymptotically optimal number of comparisons and with the number of moves independent on the number of input sequences.  ...  We conjecture that, using the algorithm described here as a subroutine, it is possible to devise an asymptotically efficient multiway in-place merging algorithm.  ... 
doi:10.1007/978-3-642-03409-1_13 fatcat:3xgd5bnukjeubj3goudoar3bnu

A Heapify Based Parallel Sorting Algorithm

Mwaffaq A. Abu Al hija, Arwa Zabian, Sami Qawasmeh, Omer H. Abu Al haija
2008 Journal of Computer Science  
Quick sort is a sorting algorithm whose worst case running time is (n 2 ) on an input array of n numbers. It is the best practical for sorting because it has the advantage of sorting in place.  ...  Problem statement: Behavior of quick sort is complex, we proposed in-place 2m threads parallel heap sort algorithm which had advantage in sorting in place and had better performance than classical sequential  ...  In [10] , is proposed ultimate heap sort that is a variant of heap sort that sorts n elements in (nlog 2 (n+1)) time in the worst case by performing at most nlog 2 n+θ(n) key comparisons and nlog 2 n  ... 
doi:10.3844/jcssp.2008.897.902 fatcat:72zsdm5tyrbipfm3ykwce7ieci

Exploiting few inversions when sorting: Sequential and parallel algorithms

Christos Levcopoulos, Ola Petersson
1996 Theoretical Computer Science  
X can be sorted in-place, i.e. using only O(logn) bits of extra space, in time O(n log (Znv(X)/n)), which is optimal with respect to the number of inversions.  ...  Given p processors on an EREW PRAM, X can be sorted in time 0 n log(z~wM> ( flog n , P 1 which is optimal with respect to the number of inversions.  ...  Introduction It is well known that Sl(nlog n) time is necessary to sort n elements in both the worst case and the average case in a comparison-based model of computation [21] .  ... 
doi:10.1016/0304-3975(95)00256-1 fatcat:b32pw364yvgzhasajak577nvai

Efficient Algorithms for Two Generalized 2-Median Problems on Trees [chapter]

Shan-Chyun Ku, Chi-Jen Lu, Biing-Feng Wang, Tzu-Chin Lin
2001 Lecture Notes in Computer Science  
For this problem, Tamir [14] had an O(pn 2 )-time algorithm, while Gavish and Sridhar [6] had an O(nlog n)-time algorithm for the case of p=2.  ...  We solve both generalizations in O(nlog n) time, improving the previous ones from O(n 2 ). We also study cases when linear time algorithms exist for the 2-median problem and the two generalizations.  ...  Gavish and Sridhar had an O(nlog n)-time algorithm, which runs Step 1 and 3 in O(n) time but needs O(nlog n) time for Step 2.  ... 
doi:10.1007/3-540-45678-3_65 fatcat:rxfrb2otfjf6plxigoyt7v2ujq

Computing with Noisy Information

Uriel Feige, Prabhakar Raghavan, David Peleg, Eli Upfal
1994 SIAM journal on computing (Print)  
Each leaf is labeled with a permutation representing the sorted order for the input (for sorting and merging) or an index in [1, N] (for selection and searching). A simple example is in order here.  ...  In the noisy comparison tree model, tight bounds are given on the number of noisy comparisons for searching, sorting, selection and merging.  ...  We thank Noga Alon and Yossi Azar for helpful discussions, and for directing us to some of the references.  ... 
doi:10.1137/s0097539791195877 fatcat:qgqcx6bp75cohevdyibuvoq44m

Association of Moving Objects Across Visual Sensor Networks

Muhammad J. Mirza, Nadeem Anjum
2012 Journal of Multimedia  
normally distributed, with zero mean and variance σ 2 , we have: AIC(p; α) = K(n,σ) + R p /σ 2 + αp, (4) where K(n,σ) = nlog(2πσ 2 ) is a constant depending on the marginals of thexs.  ...  On lattice complexity, the computation process of this algorithm requires two matrixes with lattice size M×N and a matrix with size M×N×8, the algorithm in the lattice complexity is O (M×N) ; It can be  ...  Service ontology mapping mechanism is analyzed in detail and semantic model is built with the study of the correlation across the geometry modeling service.  ... 
doi:10.4304/jmm.7.1.2-8 fatcat:4cc7sala7ffixohi3ccvothajm

Selection from read-only memory and sorting with minimum data movement

J.Ian Munro, Venkatesh Raman
1996 Theoretical Computer Science  
These include an O(n"E) worst case algorithm and an O(n log log n) average case algorithm, both using a constant number of extra storage cells or indices.  ...  Here, we consider the scenario in which the data resides in an array of read-only memory and hence the elements cannot be moved within the array.  ...  An array of n items can be sorted using O(n2 ) comparisons, 0( 1) indices, and 13n/2J data moves in the worst case. Proof. We place elements of a non-trivial cycle as follows.  ... 
doi:10.1016/0304-3975(95)00225-1 fatcat:cmbezgl5cfbdrgjljr6hdmrv4m

Scalable parallel formulations of the barnes-hut method for n-body simulations

Ananth Y. Grama, Vipin Kumar, Ahmed Sameh
1994 Supercomputing, Proceedings  
Coupled with parallel processing, these techniques hold the promise of large scale n-body simulations.  ...  We present an experimental evaluation of our schemes on a 256 processor nCUBE2 and a 256 processor CM5.  ...  This work is also sponsored in part by MSI. Access to computing facilities was provided by Cray Research and by the Pittsburgh Supercomputing C enter.  ... 
doi:10.1145/602843.602846 fatcat:qguwievrqnfo3dqxxbck7leury
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