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Sorting Selection and Routing on the Array with Reconfigurable Optical Buses
"... In this paper we present efficient algorithms for sorting, selection and packet routing on the AROB (Array with Reconfigurable Optical Buses) model. ..."
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Cited by 32 (5 self)
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In this paper we present efficient algorithms for sorting, selection and packet routing on the AROB (Array with Reconfigurable Optical Buses) model.
Selection Algorithms for Parallel Disk Systems
, 1998
"... this paper we present deterministic and randomized selection algorithms for parallel disk systems. The algorithms to be presented, in addition to being asymptotically optimal, have small underlying constants in their time bounds and hence have the potential of being practical. ..."
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Cited by 11 (3 self)
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this paper we present deterministic and randomized selection algorithms for parallel disk systems. The algorithms to be presented, in addition to being asymptotically optimal, have small underlying constants in their time bounds and hence have the potential of being practical.
Selection, Routing, and Sorting on the Star Graph
 Proceedings of the International Parallel Processing Symposium
, 1993
"... We consider the problems of selection, routing and sorting on an nstar graph (with n! nodes),an interconnection network which has been proven to possess many special properties. We identify a tree like subgraph (which we call as a ‘(k, 1,k) chain network’) of the star graph which enables us to desi ..."
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Cited by 10 (3 self)
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We consider the problems of selection, routing and sorting on an nstar graph (with n! nodes),an interconnection network which has been proven to possess many special properties. We identify a tree like subgraph (which we call as a ‘(k, 1,k) chain network’) of the star graph which enables us to design efficient algorithms for the above mentioned problems. We present an algorithm that performs a sequence of n prefix computations in O(n 2) time. This algorithm is used as a subroutine in our other algorithms. We also show that sorting can be performed on the nstar graph in time O(n 3) and that selection of a set of uniformly distributed n keys can be performed in O(n 2) time with high probability. Finally, we also present a deterministic (non oblivious) routing algorithm that realizes any permutation in O(n 3) steps on the nstar graph. There exists an algorithm in the literature that can perform a single prefix computation in O(n lg n) time. The best known previous algorithm for sorting has a run time of O(n 3 lg n) and is deterministic. To our knowledge, the problem of selection has not been considered before on the star graph. 1
Permutation routing and sorting on the reconfigurable mesh
 International Journal of Foundations of Computer Science
, 1992
"... Abstract In this paper we demonstrate the power of reconfiguration by presenting efficient randomized algorithms for both packet routing and sorting on a reconfigurable mesh connected computer. The run times of these algorithms are better than the best achievable time bounds on a conventional mesh. ..."
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Cited by 9 (3 self)
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Abstract In this paper we demonstrate the power of reconfiguration by presenting efficient randomized algorithms for both packet routing and sorting on a reconfigurable mesh connected computer. The run times of these algorithms are better than the best achievable time bounds on a conventional mesh. Many variations of the reconfigurable mesh can be found in the literature. We define yet another variation which we call as Mr. Wealsomakeuseofthestandard PARBUS model. We showthat permutation routing problem can be solved on a linear array Mr of size n in 3n steps, whereas n − 1 is the best possible run time without recon4 figuration. A trivial lower bound for routing on Mr will be n 2.OnthePARBUS linear array, n is a lower bound and hence any standard nstep routing algorithm will be optimal. We also showthat permutation routing on an n × n reconfigurable mesh Mr can be done in time n + o(n) using a randomized algorithm or in time 1.25n + o(n) deterministically. In contrast, 2n − 2 is the diameter of a conventional mesh and hence routing and sorting will need at least 2n−2 steps on a conventional mesh. A lower bound of n 2 is in effect for routing on the 2D mesh Mr as well. On the other 1 hand, n is a lower bound for routing on the PARBUS and our algorithms have the same time bounds on the PARBUS as well. Thus our randomized routing algorithm is optimal upto a lower order term. In addition we show that the problem of sorting can be solved in randomized time n + o(n) onMr as well as on PARBUS. Clearly, this sorting algorithm will be optimal on the PARBUS model. The time bounds of our randomized algorithms hold with high probability.
Randomized Selection on the Hypercube
, 1996
"... In this paper we present randomized algorithms for selection on the hypercube. We identify two variants of the hypercube namely, the sequential model and the parallel model. In the sequential model, any node at any time can handle only communication along a single incident edge, whereas in the paral ..."
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Cited by 4 (1 self)
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In this paper we present randomized algorithms for selection on the hypercube. We identify two variants of the hypercube namely, the sequential model and the parallel model. In the sequential model, any node at any time can handle only communication along a single incident edge, whereas in the parallel model a node can communicate along all its incident edges at the same time. We specify three variations of the parallel model and present optimal randomized algorithms on all these three versions of parallel model. In particular, we show that selection on an input of size n can be performed on a pnode hypercube in time O( n p + log p) with high probability, on any of the three versions of the parallel model. This result is important in view of a lower bound that implies that selection needs\Omega\Gammae n=p) log log p + log p) time on a pnode sequential hypercube. We modify our selection algorithm to run on the sequential hypercube in which case it runs in an expected time nearly ma...
Fast Algorithms for Generating Discrete Random Variates with Changing Distributions
 ACM Transaction on Modeling and Computer Simulation
, 1993
"... One of the most fundamental operations when simulating a stochastic discreteevent dynamic system is the generation of a nonuniform discrete random variate. The simplest form of this operation can be stated as follows: Generate a random variable X which is distributed over the integers 1; 2; : : : ; ..."
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Cited by 4 (1 self)
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One of the most fundamental operations when simulating a stochastic discreteevent dynamic system is the generation of a nonuniform discrete random variate. The simplest form of this operation can be stated as follows: Generate a random variable X which is distributed over the integers 1; 2; : : : ; n such that P (X = i) = a i =(a 1 + \Delta \Delta \Delta +a n ), where the a i 's are fixed nonnegative numbers. The wellknown `alias algorithm' is available to accomplish this task in O(1) time. A more difficult problem is to generate variates for X when the a i 's are changing with time. We present three rejectionbased algorithms for this task, and for each algorithm we characterize the performance in terms of acceptance probability and the expected effort to generate a variate. We show that, under fairly unrestrictive conditions, the longrun expected effort is O(1). Applications to Markovian queueing networks are discussed. We also compare the three algorithms with competing schemes ...
An Improved Randomized Selection Algorithm With an Experimental Study
 In Proc. The 2nd Workshop on Algorithm Engineering and Experiments (ALENEX00
, 2000
"... This paper presents an efficient randomized highlevel parallel algorithm for finding the median given a set of elements distributed across a parallel machine. In fact, our algorithm solves the general selection problem that requires the determination of the element of rank k, for an arbitrarily giv ..."
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Cited by 3 (3 self)
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This paper presents an efficient randomized highlevel parallel algorithm for finding the median given a set of elements distributed across a parallel machine. In fact, our algorithm solves the general selection problem that requires the determination of the element of rank k, for an arbitrarily given integer k. Our general...
PDM Sorting Algorithms That Take A Small Number Of Passes
 PASSES, PROC. INTERNATIONAL PARALLEL AND DISTRIBUTED PROCESSING SYMPOSIUM (IPDPS
, 2005
"... We live in an era of data explosion that necessitates the discovery of novel outofcore techniques. The I/O bottleneck has to be dealt with in developing outofcore methods. The Parallel Disk Model (PDM) has been proposed to alleviate the I/O bottleneck. Sorting is an important problem that has ub ..."
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Cited by 3 (1 self)
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We live in an era of data explosion that necessitates the discovery of novel outofcore techniques. The I/O bottleneck has to be dealt with in developing outofcore methods. The Parallel Disk Model (PDM) has been proposed to alleviate the I/O bottleneck. Sorting is an important problem that has ubiquitous applications. Several asymptotically optimal PDM sorting algorithms are known and now the focus has shifted to developing algorithms for problem sizes of practical interest. In this paper we present several novel algorithms for sorting on the PDM that take only a small number of passes through the data. We also present a generalization of the zeroone principle for sorting. A shuffling lemma is presented as well. These lemmas should be of independent interest for average case analysis of sorting algorithms as well as for the analysis of randomized sorting algorithms.
Randomized routing, selection, and sorting on the otismesh
 IEEE Transactions On Parallel And Distributed Systems
, 1998
"... The Optical Transpose Interconnection System (OTIS) is a recently proposed model of computing that exploits the special features of both electronic and optical technologies. In this paper we present efficient algorithms for packet routing, sorting, and selection on the OTISMesh. The diameter of an ..."
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Cited by 2 (1 self)
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The Optical Transpose Interconnection System (OTIS) is a recently proposed model of computing that exploits the special features of both electronic and optical technologies. In this paper we present efficient algorithms for packet routing, sorting, and selection on the OTISMesh. The diameter of an N 2processor OTISMesh is 4 √ N − 3. We present an algorithm for routing any partial permutation in 4 √ N +o ( √ N) time. Our selection algorithm runs in time 6 √ N + o ( √ N) and our sorting algorithm runs in 8 √ N + o ( √ N) time. All these algorithms are randomized and the stated time bounds hold with high probability. Also, the queue size needed for these algorithms is O(1) with high probability.
Abstract Designing Efficient Distributed Algorithms Using Sampling Techniques
"... In this paper we show the power of sampling techniques in designing efficient distributed algorithms. In particular, we show that using sampling techniques, on some networks, selection can be done in such a way that the message complexity is independent of the cardinality of the set (file), provided ..."
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Cited by 1 (0 self)
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In this paper we show the power of sampling techniques in designing efficient distributed algorithms. In particular, we show that using sampling techniques, on some networks, selection can be done in such a way that the message complexity is independent of the cardinality of the set (file), provided the file size is polynomial in the networksize. For example, given afileF of size n andanintegerk(1 ≤ k ≤ n), on a pprocessor de Bruijn network, our deterministic selection algorithm can find the kth smallest key from F using O(p log 3 p) messages and with a communication delay of O(log 3 p), and that our randomized selection algorithm can finish the same taskusing only O(p) messages and a communication delay of O(log p) with high probability, provided the file size is polynomial in networksize. Our randomized selection outperforms the existing approaches in terms of both message complexity and communication delay. The property that the number of messages needed and the communication delay are independent of the size of the file makes our distributed selection schemes extremely attractive in such domains as very large database systems. Making use of our selection algorithms to select pivot element(s), we also develop a near optimal quicksortbased sorting scheme and a nearly optimal enumeration sorting scheme for sorting large distributed files on the hypercube and de Bruijn networks. Our algorithms are fully distributed without any aprioricentral control. 1