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A New Computation Model for RackBased Computing
"... Implementations of mapreduce are being used to perform many operations on very large data. We explore alternative ways that a system could use the environment and capabilities of mapreduce implementations such as Hadoop, yet perform operations that are not identical to mapreduce. In particular, w ..."
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Implementations of mapreduce are being used to perform many operations on very large data. We explore alternative ways that a system could use the environment and capabilities of mapreduce implementations such as Hadoop, yet perform operations that are not identical to mapreduce. In particular, we look at strategies for taking the join of several relations and sorting large sets. The centerpiece of this exploration is a computational model that captures the essentials of the environment in which systems like Hadoop operate. Files are unordered sets of tuples that can be read and/or written in parallel; processes are limited in the amount of input/output they can perform, and processors are available in essentially unlimited supply. In our study, we focus on communication among processes and processing time costs, both total and elapsed. We show tradeoffs among them depending on the computational limits we invoke on the processes. 1.
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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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.
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, data ..."
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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(n 2 log n) expected time in order to succeed, and that in O(n 2 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. 1
A New Computation Model for Cluster Computing
, 2009
"... Implementations of mapreduce are being used to perform many operations on very large data. We explore alternative ways that a system could use the environment and capabilities of mapreduce implementations such as Hadoop, yet perform operations that are not identical to mapreduce. The centerpiece ..."
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Implementations of mapreduce are being used to perform many operations on very large data. We explore alternative ways that a system could use the environment and capabilities of mapreduce implementations such as Hadoop, yet perform operations that are not identical to mapreduce. The centerpiece of this exploration is a computational model that captures the essentials of the environment in which systems like Hadoop operate. Files are unordered sets of tuples that can be read and/or written in parallel; processes are limited in the amount of input/output they can perform, and processors are available in essentially unlimited supply. We develop, in this model, an algorithm for sorting that has a worstcase running time better than the obvious implementations of parallel sorting. 1
AverageCase Complexity of Shellsort (Preliminary Version)
, 1999
"... Abstract. We prove a general lower bound on the averagecase complexity of Shellsort: the average number of datamovements (and comparisons) made by a ppass Shellsort for any incremental sequence is Ω(pn 1+1/p) for every p. The proof method is an incompressibility argument based on Kolmogorov compl ..."
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Abstract. We prove a general lower bound on the averagecase complexity of Shellsort: the average number of datamovements (and comparisons) made by a ppass Shellsort for any incremental sequence is Ω(pn 1+1/p) for every p. The proof method is an incompressibility argument based on Kolmogorov complexity. Using similar techniques, the averagecase complexity of several other sorting algorithms is analyzed. 1