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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 34 (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.
Derivation of Randomized Sorting and Selection Algorithms
, 1993
"... In this paper we systematically derive randomized algorithms (both sequential and parallel) for sorting and selection from basic principles and fundamental techniques like random sampling. We prove several sampling lemmas which will find independent applications. The new algorithms derived here are ..."
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Cited by 30 (28 self)
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In this paper we systematically derive randomized algorithms (both sequential and parallel) for sorting and selection from basic principles and fundamental techniques like random sampling. We prove several sampling lemmas which will find independent applications. The new algorithms derived here are the most efficient known. From among other results, we have an efficient algorithm for sequential sorting. The problem of sorting has attracted so much attention because of its vital importance. Sorting with as few comparisons as possible while keeping the storage size minimum is a long standing open problem. This problem is referred to as ‘the minimum storage sorting ’ [10] in the literature. The previously best known minimum storage sorting algorithm is due to Frazer and McKellar [10]. The expected number of comparisons made by this algorithm is n log n + O(n log log n). The algorithm we derive in this paper makes only an expected n log n + O(n ω(n)) number of comparisons, for any function ω(n) that tends to infinity. A variant of this algorithm makes no more than n log n + O(n log log n) comparisons on any input of size n with overwhelming probability. We also prove high probability bounds for several randomized algorithms for which only expected bounds have been proven so far.
On VLSI Layouts Of The Star Graph And Related Networks
, 1994
"... . We prove that the minimal VLSI layout of the arrangement graph A(n; k) occupies \Theta(n!=(n \Gamma k \Gamma 1)!) 2 area. As a special case we obtain an optimal layout for the star graph S n with the area \Theta(n!) 2 : This answers an open problem posed by Akers, Harel and Krishnamurthy [1]. ..."
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Cited by 18 (3 self)
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. We prove that the minimal VLSI layout of the arrangement graph A(n; k) occupies \Theta(n!=(n \Gamma k \Gamma 1)!) 2 area. As a special case we obtain an optimal layout for the star graph S n with the area \Theta(n!) 2 : This answers an open problem posed by Akers, Harel and Krishnamurthy [1]. The method is also applied to the pancake graph. The results provide optimal upper and lower bounds for crossing numbers of the above graphs. Key Words: area, arrangement graph, congestion, crossing number, embedding, layout, pancake graph, star graph, VLSI 1
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...
EFFICIENT SORTING ON THE STAR GRAPH INTERCONNECTION NETWORK
, 1997
"... Two algorithms for sorting n! numbers on an nstar interconnection network are described. Both algorithms are based on arranging the n! processors of the nstar in a virtual (n \Gamma 1)dimensional array. The first algorithm runs in O(n 3 log n) time. This performance matches that of the fastest ..."
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Cited by 3 (0 self)
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Two algorithms for sorting n! numbers on an nstar interconnection network are described. Both algorithms are based on arranging the n! processors of the nstar in a virtual (n \Gamma 1)dimensional array. The first algorithm runs in O(n 3 log n) time. This performance matches that of the fastest previously known algorithm for the same problem. In addition to providing a new paradigm for sorting on the nstar, the proposed algorithm has the advantage of being considerably simpler to state while requiring no recursion in its formulation. Its idea is to sort the input by repeatedly sorting the contents of all rows in each dimension of the (n \Gamma 1)dimensional array. The second algorithm presented in this paper is more efficient. It runs in O(n 2 ) time and thus provides an asymptotic improvement over its predecessors. However, it is more elaborate as it uses an existing result for sorting optimally on an (n \Gamma 1)dimensional array.
unknown title
, 2003
"... An improved, randomized algorithm for parallel selection with an experimental study � ..."
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An improved, randomized algorithm for parallel selection with an experimental study �
Unifying Themes for Network Selection 1
"... Abstract. In this paper we present efficient deterministic and randomized algorithms for selection on any interconnection network when the number of input keys (n) is ≥ the number of processors (p). Our deterministic algorithm runs on any network in time O ( n log n), where p log log p + T s p T s p ..."
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Abstract. In this paper we present efficient deterministic and randomized algorithms for selection on any interconnection network when the number of input keys (n) is ≥ the number of processors (p). Our deterministic algorithm runs on any network in time O ( n log n), where p log log p + T s p T s p is the time needed for sorting p keys using p processors (assuming that broadcast and prefix computations take time less than or equal to T s p). As an example, our algorithm runs on a √ p × √ p mesh in time O ( n p log log p + √ p log n), where n is the input size. This time bound is nearly optimal and significantly better than that of the best existing algorithmwhen n is large. On the other hand, our randomized algorithm runs in an expected time of O( ( n p + is the time needed for collecting and T s sparse)loglogp) onanynetwork,whereTs sparse sorting p1−ɛ sample keys using p processors. (Here ɛ is a constant < 1). On a √ p × √ n p mesh our algorithm runs in an expected O( ( p + √ p)loglogp) time, a significant improvement over the deterministic algorithm. We have implemented our randomized algorithm on the Connection Machine CM2. Experimental results obtained are promising. In this paper we also report our implementation details. 1
Unifying Themes For Selection On Any Network 1
"... Abstract. In this paper we present efficient deterministic and randomized algorithms for selection on any interconnection network when the number of input keys (n) is ≥ the number of processors (p). Our deterministic algorithm runs on any network in time O ( n p log log p + T s p log n), where T s p ..."
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Abstract. In this paper we present efficient deterministic and randomized algorithms for selection on any interconnection network when the number of input keys (n) is ≥ the number of processors (p). Our deterministic algorithm runs on any network in time O ( n p log log p + T s p log n), where T s p is the time needed for sorting p keys using p processors. On the other hand, our randomized algorithm runs in an expected time of O( ( n p sparse + Tp)loglogp) onanynetwork,whereTsparse p is the time needed for collecting and sorting p 1−ɛ sample keys using p processors. (Here ɛ is a constant < 1). Application of the above algorithms on the mesh and the hypercube yield better results than known before. We have implemented our randomized algorithm on the Connection Machine CM2. Experimental results obtained
Reliable Communication in Faulty Star Networks
"... Abstract ‘ We take advantage of the hierarchical structure of the star graph network to obtain an efficient method for constructing nodedisjoint paths between arbitrary pairs of nodes in the network. A distributed faulttolerant routing algorithm for the star network based on this construction metho ..."
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Abstract ‘ We take advantage of the hierarchical structure of the star graph network to obtain an efficient method for constructing nodedisjoint paths between arbitrary pairs of nodes in the network. A distributed faulttolerant routing algorithm for the star network based on this construction method is then presented and evaluated. The proposed algorithm adapts the routing decisions in response to node failures. Node failure and repair conditions may arise dynamically (at any time) provided that the total number of faulty nodes at any given time is less than the nodeconnectivity n1 of the nstar. We show that if the node failures occur ’reasonably … apart in time, then all messages will be routed on paths of length δ + ε where δ is the minimum distance between the source and the destination and ε is 0, 2, or 4. In the unlikely case where more failures occur in a ’short period…, the algorithm still delivers all messages but via possibly longer paths. Index Terms ‘ Fault tolerance, star graph, routing, nodedisjoint paths, distributed algorithm. 1.
AlgorithmBased FaultTolerant Strategies in Faulty Hypercube and Star Graph Multicomputers
, 1996
"... This dissertation addresses the design of algorithmbased faulttolerant strategies in faulty hypercube and star graph multicomputers without hardware modification. Several new concepts and designs are presented here under the permanent and transient fault models. Under the permanent fault model, we ..."
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This dissertation addresses the design of algorithmbased faulttolerant strategies in faulty hypercube and star graph multicomputers without hardware modification. Several new concepts and designs are presented here under the permanent and transient fault models. Under the permanent fault model, we propose a new faulttolerant reconfiguration scheme in the faulty hypercube and star graph multicomputers. The reconfiguration scheme is to identify new reconfiguration architectures, namely maximal faultfree subcubering and substarring, to tolerate faults in hypercubes and star graphs. The maximal faultfree subcubering and substarring are connected by a ring of maximal faultfree subcubes and virtual substars, respectively. The reconfiguration scheme can tolerate arbitrarily number of faults. This is the first result to derive a reconfiguration scheme with high processor utilization and low performance slowdown. To demonstrate the faulttolerant capability of the scheme, two applicati...