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Algorithmic Complexity
 M B
, 1993
"... The theory of algorithmic complexity (commonly known as Kolmogorov complexity) or algorithmic information theory is a novel mathematical approach combining the theory of computation with information theory. It is the theory that finally formalizes the elusive notion of the amount of information in i ..."
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Cited by 15 (10 self)
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The theory of algorithmic complexity (commonly known as Kolmogorov complexity) or algorithmic information theory is a novel mathematical approach combining the theory of computation with information theory. It is the theory that finally formalizes the elusive notion of the amount of information in individual objects, in contrast to entropy that is a statistical notion of average code word length to transmit a message form a random source. This powerful new theory has successfully resolved ancient questions about the nature of randomness of individual objects, inductive reasoning and prediction, and has applications in mathematics, computer science, physics, biology, and other sciences, including social and behavioral sciences.
Randomized Shellsort: A simple oblivious sorting algorithm
 In Proceedings 21st ACMSIAM Symposium on Discrete Algorithms (SODA
, 2010
"... In this paper, we describe a randomized Shellsort algorithm. This algorithm is a simple, randomized, dataoblivious version of the Shellsort algorithm that always runs in O(n log n) time and succeeds in sorting any given input permutation with very high probability. Taken together, these properties ..."
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Cited by 12 (2 self)
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In this paper, we describe a randomized Shellsort algorithm. This algorithm is a simple, randomized, dataoblivious version of the Shellsort algorithm that always runs in O(n log n) time and succeeds in sorting any given input permutation with very high probability. Taken together, these properties imply applications in the design of new efficient privacypreserving computations based on the secure multiparty computation (SMC) paradigm. In addition, by a trivial conversion of this Monte Carlo algorithm to its Las Vegas equivalent, one gets the first version of Shellsort with a running time that is provably O(n log n) with very high probability. 1
AverageCase Analysis of Algorithms Using Kolmogorov Complexity
 JOURNAL OF COMPUTER SCIENCE AND TECHNOLOGY
, 2000
"... Analyzing the averagecase complexity of algorithms is a very practical but very difficult problem in computer science. In the past few years, we have demonstrated that Kolmogorov complexity is an important tool for analyzing the averagecase complexity of algorithms. We have developed the incomp ..."
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Cited by 4 (2 self)
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Analyzing the averagecase complexity of algorithms is a very practical but very difficult problem in computer science. In the past few years, we have demonstrated that Kolmogorov complexity is an important tool for analyzing the averagecase complexity of algorithms. We have developed the incompressibility method [7]. In this paper, we use several simple examples to further demonstrate the power and simplicity of such method. We prove bounds on the averagecase number of stacks (queues) required for sorting sequential or parallel Queueusort or Stacksort.
Spinthebottle Sort and Annealing Sort: Oblivious Sorting via Roundrobin Random Comparisons
"... We study sorting algorithms based on randomized roundrobin comparisons. Specifically, we study Spinthebottle sort, where comparisons are unrestricted, and Annealing sort, where comparisons are restricted to a distance bounded by a temperature parameter. Both algorithms are simple, randomized, dat ..."
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Cited by 1 (0 self)
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We study sorting algorithms based on randomized roundrobin comparisons. Specifically, we study Spinthebottle sort, where comparisons are unrestricted, and Annealing sort, where comparisons are restricted to a distance bounded by a temperature parameter. Both algorithms are simple, randomized, dataoblivious sorting algorithms, which are useful in privacypreserving computations, but, as we show, Annealing sort is much more efficient. We show that there is an input permutation that causes Spinthebottle sort to require Ω(n² log n) expected time in order to succeed, and that in O(n² log n) time this algorithm succeeds with high probability for any input. We also show there is an specification of Annealing sort that runs in O(n log n) time and succeeds with very high probability.
Analysis of Sorting Algorithms by Kolmogorov Complexity  A Survey
, 2003
"... Recently, many results on the computational complexity of sorting algorithms were obtained using Kolmogorov complexity (the incompressibility method). Especially, the usually hard averagecase analysis is ammenable to this method. Here we survey such results about Bubblesort, Heapsort, Shellsort, ..."
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Cited by 1 (0 self)
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Recently, many results on the computational complexity of sorting algorithms were obtained using Kolmogorov complexity (the incompressibility method). Especially, the usually hard averagecase analysis is ammenable to this method. Here we survey such results about Bubblesort, Heapsort, Shellsort, Dobosiewiczsort, Shakersort, and sorting with stacks and queues in sequential or parallel mode. Especially in the case of Shellsort the uses of Kolmogorov complexity surprisingly easily resolved problems that had stayed open for a long time despite strenuous attacks.
method
"... Background: Although a variety of methods and expensive kits are available, molecular cloning can be a timeconsuming and frustrating process. Results: Here we report a highly simplified, reliable, and efficient PCRbased cloning technique to insert any DNA fragment into a plasmid vector or into a ge ..."
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Background: Although a variety of methods and expensive kits are available, molecular cloning can be a timeconsuming and frustrating process. Results: Here we report a highly simplified, reliable, and efficient PCRbased cloning technique to insert any DNA fragment into a plasmid vector or into a gene (cDNA) in a vector at any desired position. With this method, the vector and insert are PCR amplified separately, with only 18 cycles, using a high fidelity DNA polymerase. The amplified insert has the ends with ~16base overlapping with the ends of the amplified vector. After DpnI digestion of the mixture of the amplified vector and insert to eliminate the DNA templates used in PCR reactions, the mixture is directly transformed into competent E. coli cells to obtain the desired clones. This technique has many advantages over other cloning methods. First, it does not need gel purification of the PCR product or linearized vector. Second, there is no need of any cloning kit or specialized enzyme for cloning. Furthermore, with reduced number of PCR cycles, it also decreases the chance of random mutations. In addition, this method is highly effective and reproducible. Finally, since this cloning method is also sequence independent, we demonstrated that it can be used for chimera construction, insertion, and multiple mutations spanning a stretch of DNA up to 120 bp.
BOLYAI SOCIETY Entropy, Search, Complexity, pp. 209–232. MATHEMATICAL STUDIES, 16 Analysis of Sorting Algorithms by Kolmogorov Complexity
"... Recently, many results on the computational complexity of sorting algorithms were obtained using Kolmogorov complexity (the incompressibility method). Especially, the usually hard averagecase analysis is ammenable to this method. Here we survey such results about Bubblesort, Heapsort, Shellsort, Do ..."
Abstract
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Recently, many results on the computational complexity of sorting algorithms were obtained using Kolmogorov complexity (the incompressibility method). Especially, the usually hard averagecase analysis is ammenable to this method. Here we survey such results about Bubblesort, Heapsort, Shellsort, Dobosiewiczsort, Shakersort, and sorting with stacks and queues in sequential or parallel mode. Especially in the case of Shellsort the uses of Kolmogorov complexity surprisingly easily resolved problems that had stayed open for a long time despite strenuous attacks. 1.
A Complete Bibliography of Publications in Journal of Computational Chemistry: 1990–1999
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