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Average-case analysis of algorithms using Kolmogorov complexity

Tao Jiang, Ming Li, Paul M. B. Vitányi
2000 Journal of Computer Science and Technology  
We prove bounds on the average-case number of stacks (queues) required for sorting sequential or parallel Queuesort or Stacksort.  ...  Analyzing the average-case complexity of algorithms is a very practical but very difficult problem in computer science.  ...  Average Case of Bubble Sort: An Example Generally speaking, the difficulty of analyzing the average-case complexity comes from the fact that one has to analyze the time complexity for all inputs of each  ... 
doi:10.1007/bf02950402 fatcat:cvy26nh7vvcqplghhzg55mupum

A survey of randomness and parallelism in comparison problems [chapter]

Danny Krizanc
1998 Lecture Notes in Computer Science  
A survey of results for the problems of selection, merging and sorting in the Randomized Parallel Comparison Tree RPCT model is given.  ...  The results indicate that while randomization helps" in the case of selection, it does not provide any advantage for the cases of merging and sorting, in this model.  ...  parallel complexity of either merging or sorting, in the PCT model.  ... 
doi:10.1007/3-540-64359-1_703 fatcat:igwdbljwqrhpvejxczrsioofne

Average-Case Complexity of Shellsort (Preliminary Version) [chapter]

Tao Jiang, Ming Li, Paul Vitányi
1999 Lecture Notes in Computer Science  
The proof method is an incompressibility argument based on Kolmogorov complexity. Using similar techniques, the average-case complexity of several other sorting algorithms is analyzed.  ...  We prove a general lower bound on the average-case complexity of Shellsort: the average number of data-movements (and com-paris~ns) made by a p-pass Shellsort for any incremental sequence is fl(pn HIP)  ...  This requires that (approximately) m :S efo = O(yri,).This yields an average complexity of Parallel-Stack-Sort of: On the average, the number of parallel stacks required to sort a permutation is D ( fo  ... 
doi:10.1007/3-540-48523-6_42 fatcat:seetfrrgunhx7m7clhdqstqkda

Average-Case Complexity of Shellsort [article]

Tao Jiang, Paul Vitanyi (CWI, U of Amsterdam)
1999 arXiv   pre-print
Using similar arguments, we analyze the average-case complexity of several other sorting algorithms.  ...  We prove a general lower bound on the average-case complexity of Shellsort: the average number of data-movements (and comparisons) made by a p-pass Shellsort for any incremental sequence is Ω (pn^1 + 1  ...  Sedgewick for telling us many things about Shellsort and stack/queue sorts.  ... 
arXiv:cs/9901010v1 fatcat:3hsatxce2jhbvcwmkedlbkd5um

Parallel comparison merging of many-ordered lists

Y. Azar
1991 Theoretical Computer Science  
., Parallel comparison merging of many-ordered lists (Note), Theoretical Computer Science 83 (1991) 275-285.  ...  Berkman for bringing the problem considered in this paper to my attention and M. Paterson for helpful remarks.  ...  Theorem 3.3 for m = n is the main result of [2] for the average case complexity of sorting, i.e. that the average case complexity of sorting n elements requires In order to prove Theorem 3.3 we use the  ... 
doi:10.1016/0304-3975(91)90279-b fatcat:3l34djesvrb5vezpizdyzios3y

Analysis of Sorting Algorithms by Kolmogorov Complexity (A Survey) [article]

Paul M.B. Vitanyi
2009 arXiv   pre-print
Recently, many results on the computational complexity of sorting algorithms were obtained using Kolmogorov complexity (the incompressibility method).  ...  Especially, the usually hard average-case analysis is ammenable to this method.  ...  Hence, the average complexity of Parallel-Stack-Sort is O( √ n) · n − 1 n + n · 1 n = O( √ n). 2 Theorem 6 On average (uniform distribution), the number of parallel stacks required to sort a permutation  ... 
arXiv:0905.4452v1 fatcat:amug6iugczdb3b65kxjrxuemwu

Performance Evaluation of Parallel Sorting Algorithms on IMAN1 Supercomputer

Maha Saadeh, Huda Saadeh, Mohammad Qatawneh
2016 International Journal of Advanced Science and Technology  
Results show that the run time of parallel Quicksort algorithm outperforms both Merge sort and Merge-Quicksort algorithms.  ...  Moreover, on large number of processors, parallel Quicksort achieves the best parallel efficiency of up to 88%, while Merge sort and Merge-Quicksort algorithms achieve up to 49% and 52% parallel efficiency  ...  The time complexity is O(n 2 ). Figure 5 illustrate the complexity of Quicksort in the best case and average case, respectively.  ... 
doi:10.14257/ijast.2016.95.06 fatcat:u7ite3chd5hkbnhmjf4mdw5cye

Performance Evaluation of Parallel Bubble Sort Algorithm on Supercomputer IMAN1

Reem Saadeh, Mohammad Qatawneh
2019 Social Science Research Network  
Parallel sorting algorithms order a set of elements USING MULTIPLE processors in order to enhance the performance of sequential sorting algorithms.  ...  In this paper, the running time, parallel speedup and parallel efficiency OF PARALLEL bubble sort is evaluated and measured.  ...  Sequential Bubble Sort Analysis Bubble sort has worst-case and average complexity both О(n 2 ), where n is the number of items being sorted.  ... 
doi:10.2139/ssrn.3423841 fatcat:ahs5e6trrre5za2o22lmlfcddy

A General Framework for Sorting Large Data Sets Using Independent Subarrays of Approximately Equal Length

Shahriar Shirvani Moghaddam, Kiaksar Shirvani Moghaddam
2022 IEEE Access  
The third experiment shows the effectiveness of the proposed parallel framework to the parallel sorting based on the random-access machine model.  ...  The time complexity analyses of the proposed framework demonstrate an improvement compared to the conventional Merge and Quick sorting algorithms.  ...  In the worst, average, and best cases of the Merge-sort, the time complexity is O(N log N ), while the time complexity for the worst-case of the Quick-sort is O(N 2 ), and that for the average and best  ... 
doi:10.1109/access.2022.3145981 fatcat:arem7eoy5zavtifdpfw5eivzse

Page 2947 of Mathematical Reviews Vol. , Issue 95e [page]

1995 Mathematical Reviews  
We study it from the point of view of average case analysis. As a matter of fact, the complexity of these algorithms varies greatly between the worst case and the best case.  ...  Summary: “The parallel complexity of various operations on sorted sets is studied. Let X and Y be two sorted sets of respective sizes n and m,n>m. W.J. Paul, U. Vishkin and H.  ... 

Effect of Parallelization, Execution Time and Inter-process Communication on Sorting Techniques using Message Passing Interface

Dev Gaurav, Sahil Arora, Prashant Gupta
2014 International Journal of Computer Applications  
Using MPI, parallelization on five sorting techniques which are selection sort, bubble sort, quick sort, insertion sort and shell sort have been implemented.  ...  So as the number of processors increase, the amount of work done by each processor will be decrease regardless the effect of the number of physical cores used.  ...  Shell Sort: Complexity: Complexity is nearly quadratic in nature. [7] Average case: approximately O(n 3/2 ) Method: • The original array is divided into sub arrays according to the span value.  ... 
doi:10.5120/17681-8524 fatcat:xbpf6sxhg5gh5jcsm3z4h3j43q

Large-small Sorting for Successive Cancellation List Decoding of Polar Codes

Kyungpil Lee, In-Cheol Park
2020 IEEE Access  
To reduce the latency of the metric sorting, this paper proposes a new sorting method derived by analyzing path extension cases encountered in SCL decoding.  ...  Combined with the state-of-the-art sorting method, the proposed method reduces the average SCL decoding latency for a (1024, 512) polar code by 33.1% when the list size is 8.  ...  The proposed method is to adaptively replace the large sorting with a parallel small sorting, which is derived by analyzing path extension cases.  ... 
doi:10.1109/access.2020.2996016 fatcat:rit4tvzjerfploeyl6vqto4rvi

Page 3790 of Mathematical Reviews Vol. , Issue 84i [page]

1984 Mathematical Reviews  
Author’s summary: “It is shown that a large class of continuous models for the average case analysis of many sorting algorithms (including quicksort, Shell’s sort, heapsort, insertion sort) will display  ...  Author’s summary: “We give a detailed survey of the small number of existing papers on parallel methods of merging and sorting data files in the internal storage of multiprocessor computers.  ... 

Noisy sort, a memory-intensive sorting algorithm

Susumu Horiguchi, Williard L. Miranker
1989 Linear Algebra and its Applications  
A table-lookup technique for sorting is developed. It is a highly parallel method which develops an approximation to the sort through a single access to an associative memory.  ...  A postprocessing step is intended to complete the sort. The scheme is most effective for special data classes.  ...  The authors thank Dr. Craig Douglas and Dr. Andrew Winkler for stimulating discussions on these topics.  ... 
doi:10.1016/0024-3795(89)90484-9 fatcat:dvu5alb4rzhnbo6bwgx3n6ewya

Parallel Processing of Sorting and Searching Algorithms Comparative Study

Saad AL-Azzam, Mohammad Qatawneh
2018 Modern Applied Science  
Each one of the sort and search algorithms was tested in worst, average and best case scenarios.  ...  Much of the software recently consumes a long period of time both to sort and search datasets, and thus optimizing these algorithms becomes a priority.  ...  (Kumari & Chakraborty, 2015) a statistical comparative study of sorting algorithms, viz. Quick sort, Heap sort and K sort with a study of time complexity for each optimal average case complexity.  ... 
doi:10.5539/mas.v12n4p143 fatcat:rbycnsi4jvbavbf2tmxu6w6ipy
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