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10
Packet Routing In FixedConnection Networks: A Survey
, 1998
"... We survey routing problems on fixedconnection networks. We consider many aspects of the routing problem and provide known theoretical results for various communication models. We focus on (partial) permutation, krelation routing, routing to random destinations, dynamic routing, isotonic routing ..."
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Cited by 29 (3 self)
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We survey routing problems on fixedconnection networks. We consider many aspects of the routing problem and provide known theoretical results for various communication models. We focus on (partial) permutation, krelation routing, routing to random destinations, dynamic routing, isotonic routing, fault tolerant routing, and related sorting results. We also provide a list of unsolved problems and numerous references.
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
A Lower Bound on the AverageCase Complexity of Shellsort
, 1999
"... We give 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 \Omega\Gamma pn 1+1=p ) for every p. The proof is an example of the use of Kolmogorov complexity (the incompr ..."
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Cited by 10 (6 self)
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We give 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 \Omega\Gamma pn 1+1=p ) for every p. The proof is an example of the use of Kolmogorov complexity (the incompressibility method) in the analysis of algorithms. 1 Introduction The question of a nontrivial general lower bound (or upper bound) on the average complexity of Shellsort (due to D.L. Shell [14]) has been open for about four decades [5, 13]. We present such a lower bound for ppass Shellsort for every p. Shellsort sorts a list of n elements in p passes using a sequence of increments h 1 ; : : : ; h p . In the kth pass the main list is divided in h k separate sublists of length dn=h k e, where the ith sublist consists of the elements at positions j, where j mod h k = i \Gamma 1, of the main list (i = 1; : : : ; h k ). Every sublist is sorted using a straightforward insertion sort. The effi...
A Lower Bound for Sorting Networks Based on the Shuffle Permutation
 Mathematical Systems Theory
, 1994
"... We prove an \Omega\Gamma/1 2 n= lg lg n) lower bound for the depth of ninput sorting networks based on the shuffle permutation. The best previously known lower bound was the trivial \Omega\Gammaiv n) bound, while the best upper bound is given by Batcher's \Theta(lg 2 n)depth bitonic sorting ..."
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Cited by 6 (5 self)
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We prove an \Omega\Gamma/1 2 n= lg lg n) lower bound for the depth of ninput sorting networks based on the shuffle permutation. The best previously known lower bound was the trivial \Omega\Gammaiv n) bound, while the best upper bound is given by Batcher's \Theta(lg 2 n)depth bitonic sorting network. The proof technique employed in the lower bound argument may be of independent interest. 1 Introduction A variety of different classes of sorting networks has been described in the literature. Of particular interest here are the socalled AKS network [1] discovered by Ajtai, Koml'os and Szemer'edi, and the sorting networks proposed by Batcher [2]. The AKS network is the only known sorting network with O(lg n) depth. However, the topology of the network is highly irregular, and the multiplicative constant hidden by the Onotation is impractically large [1, 11]. On the other hand, the networks proposed by Batcher have a relatively simple interconnection structure and a small constant...
P.: The averagecase complexity of Shellsort
 Lecture Notes in Computer Science 1644
, 1999
"... 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 1 1+ any incremental sequence is Ω(pn p) for all p ≤ log n. Using similar arguments, we analyze the averagecase complexity of several oth ..."
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Cited by 6 (2 self)
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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 1 1+ any incremental sequence is Ω(pn p) for all p ≤ log n. Using similar arguments, we analyze the averagecase complexity of several other sorting algorithms. 1
A SuperLogarithmic Lower Bound for Hypercubic Sorting Networks
 in Proceedings of the 21st International Colloquium on Automata, Languages, and Programming
, 1994
"... Hypercubic sorting networks are a class of comparator networks whose structure maps efficiently to the hypercube and any of its bounded degree variants. Recently, ninput hypercubic sorting networks with depth 2 O( p lg lg n) lg n have been discovered. These networks are the only known sorti ..."
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Cited by 3 (1 self)
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Hypercubic sorting networks are a class of comparator networks whose structure maps efficiently to the hypercube and any of its bounded degree variants. Recently, ninput hypercubic sorting networks with depth 2 O( p lg lg n) lg n have been discovered. These networks are the only known sorting networks of depth o(lg 2 n) that are not based on expanders, and their existence raises the question of whether a depth of O(lg n) can be achieved by any hypercubic sorting network. In this paper, we resolve this question by establishing an\Omega \Gamma lg n lg lg n lg lg lg n \Delta lower bound on the depth of any ninput hypercubic sorting network. Our lower bound can be extended to certain restricted classes of nonoblivious sorting algorithms on hypercubic machines. 1 Introduction A variety of different classes of sorting networks have been described in the literature. Of particular interest here are the socalled AKS network [1] discovered by Ajtai, Koml'os, and Szemer...
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.
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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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(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
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