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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 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.
Hypercubic Sorting Networks
 SIAM J. Comput
, 1998
"... . This paper provides an analysis of a natural dround tournamentover n = 2 d players, and demonstrates that the tournament possesses a surprisingly strong ranking property. The ranking property of this tournament is used to design efficient sorting algorithms for a variety of different models of ..."
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Cited by 14 (2 self)
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. This paper provides an analysis of a natural dround tournamentover n = 2 d players, and demonstrates that the tournament possesses a surprisingly strong ranking property. The ranking property of this tournament is used to design efficient sorting algorithms for a variety of different models of parallel computation: (i) a comparator network of depth c \Delta lg n, c 7:44, that sorts the vast majority of the n! possible input permutations, (ii) an O(lg n)depth hypercubic comparator network that sorts the vast majority of permutations, (iii) a hypercubic sorting network with nearly logarithmic depth, (iv) an O(lgn)time randomized sorting algorithm for any hypercubic machine (other such algorithms have been previously discovered, but this algorithm has a significantly smaller failure probability than any previously known algorithm), and (v) a randomized algorithm for sorting n O(m)bit records on an (n lg n)node omega machine in O(m + lg n) bit steps. Key words. parallel sort...
A Hypercubic Sorting Network with Nearly Logarithmic Depth
 In Proceedings of the 24th Annual ACM Symposium on Theory of Computing
, 1992
"... A natural class of "hypercubic" sorting networks is defined. The regular structure of these sorting networks allows for elegant and efficient implementations on any of the socalled hypercubic networks (e.g., the hypercube, shuffleexchange, butterfly, and cubeconnected cycles). This c ..."
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Cited by 8 (5 self)
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A natural class of "hypercubic" sorting networks is defined. The regular structure of these sorting networks allows for elegant and efficient implementations on any of the socalled hypercubic networks (e.g., the hypercube, shuffleexchange, butterfly, and cubeconnected cycles). This class of sorting networks contains Batcher's O(lg 2 n)depth bitonic sort, but not the O(lg n)depth sorting network of Ajtai, Koml'os, and Szemer'edi. In fact, no o(lg 2 n) depth compareinterchange sort was previously known for any of the hypercubic networks. In this paper, we prove the existence of a family of 2 O( p lg lg n) lg ndepth hypercubic sorting networks. Note that this depth is o(lg 1+ffl n) for any constant ffl ? 0. 1 Introduction A comparator network is an ninput, noutput acyclic circuit made up of wires and 2input, 2output comparator gates. The input wires of the network are numbered from 0 to n \Gamma 1, as are the output wires. The inputs to the network may be tho...
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...
A SuperLogarithmic Lower Bound for ShuffleUnshuffle Sorting Networks
, 1994
"... Shuffleunshuffle sorting networks are a class of comparator networks whose structure maps efficiently to the hypercube and any of its bounded degree variants. Recently, ninput shuffleunshuffle sorting networks with depth2O(plglgn)lgn have been discovered. These networks are the only known sorting ..."
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Shuffleunshuffle sorting networks are a class of comparator networks whose structure maps efficiently to the hypercube and any of its bounded degree variants. Recently, ninput shuffleunshuffle sorting networks with depth2O(plglgn)lgn have been discovered. These networks are the only known sorting networks of depth o(lg2n) that are not based on expanders, and their existence raises the question of whether a depth of O(lgn) can be achieved by any shuffleunshuffle sorting network. In this paper, we resolve this question by establishing lglglgnlower bound on the depth of anyninput shuffleunshuffle sorting network. Our lower bound can be extended to certain restricted classes of nonoblivious sorting algorithms on hypercubic machines.