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Deterministic 1 -k routing on meshes with applications to worm-hole routing
[chapter]

1994
*
Lecture Notes in Computer Science
*

Non-trivial extensions are given to the general l-

doi:10.1007/3-540-57785-8_145
fatcat:apson42lwrdh3emzkgmgszi4yi
*k**routing*problem and for*routing**on*higher dimensional*meshes*. ... In*1*-*k**routing*each o f t h e n 2 processing units of an n n*mesh*connected computer initially holds*1*packet which must be*routed*such t h a t a n y processor is the destination of at most*k*packets. ... The results were extended to l-*k**routing*and for*routing**on*higher dimensional*meshes*. Finally we considered*k*-*k**routing*with short working queues. ...##
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Block gossiping on grids and tori: Deterministic sorting and routing match the bisection bound
[chapter]

1993
*
Lecture Notes in Computer Science
*

This proves that all packets reach their destination row in time under distribution

doi:10.1007/3-540-57273-2_62
fatcat:i6er5xsf6vc4fhtynlc6eeuomi
*1*. A similar argument can be given for distribution 2 . 2 ... The remaining problem is now to nd a way to*route*those elements that have to travel a distance between 3n=16 and n=4. ... The techniques presented in this paper can also be used to obtain optimal*deterministic*algorithms for*k*{*k**routing**on*r-dimensional*meshes*. ...##
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Deterministic Routing with HoL-Blocking-Awareness for Direct Topologies

2013
*
Procedia Computer Science
*

Depending

doi:10.1016/j.procs.2013.05.432
fatcat:2thnl7urmjgmhf42gvqpv26yiu
*on*the number of*routing*options that packets may use,*routing*algorithms are classified into two categories. ... of*deterministic**routing*such as in-order delivery of packets and implementation simplicity. ...*k*−*1*(i.e., nodes are numbered from 0, 0, ..., 0 to*k*−*1*,*k*−*1*, ...,*k*−*1*). ...##
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Analysis of minimal path routing schemes in the presence of faults

1992
*
Discrete Applied Mathematics
*

Using this framework, we derive closed form solutions for a wide range of

doi:10.1016/0166-218x(92)90136-x
fatcat:gmcyecripfdorfrm3fmlobyfwi
*routing*schemes*on*the hypercube and*on*the twodimensional*mesh*. ... We introduce techniques for the derivation of the probabilities of successfully*routing*a single inessage using minimal path*routing*schemes. ... Note that we can easily generalize the four approaches to apply to*routing**on*a generalized*mesh*, such as the*k*-ary n-cube. ...##
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Faster deterministic sorting through better sampling

2003
*
Theoretical Computer Science
*

The method is illustrated by a detailed analysis for the cases of sorting

doi:10.1016/s0304-3975(02)00321-3
fatcat:2rfn4jbj2zdznl6xoqpax6yakq
*on**meshes*and for sorting in external memory*on*a single processor machine. ... In this paper, a reÿned*deterministic*sampling strategy is presented. ... Lemma 16 . 16 For*k*-*k*sorting*on*n × n*meshes*with M N*1*=2 ,T D2 (*k*; n) ¡ T*route*(*k*; n) + O(n) + (6:5 + 17:*1*= log*1*=2 N ) · √*k*· M + 3:6 · (*k*· log N · N=M )*1*=2 :For the values of N we consider, with ...##
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Improved bounds for routing and sorting on multi-dimensional meshes

1994
*
Proceedings of the sixth annual ACM symposium on Parallel algorithms and architectures - SPAA '94
*

We show improved bounds for

doi:10.1145/181014.181022
dblp:conf/spaa/Suel94
fatcat:gzpamh3z5nec3bpx6zkx7lsnki
*1*{*1**routing*and sorting*on*multi-dimensional*meshes*and tori. ... We give*deterministic*algorithms with running times of 5dn=4 + o(n) and 3dn=4 + o(n) for the d-dimensional*mesh*and torus, respectively, that make*one*copy of each element. ...*k*bd=4c, then there exists a*deterministic*algorithm for*k*{*k*sorting*on*the d-dimensional*mesh*with a running time of 3D=2 + o(n) that does not make any copies of the packets. ...##
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Sample sort on meshes
[chapter]

1997
*
Lecture Notes in Computer Science
*

We come with a new

doi:10.1007/bfb0002762
fatcat:jqaknhy7rjeqxckoupikkxpouu
*deterministic*sorting algorithm which performs much better than previous*ones*. The number of*routing*steps is reduced by a refined*deterministic*splitter selection. ... In this paper various algorithms for sorting*on*processor networks are considered. We focus*on**meshes*, but the results can be generalized easily to other decomposable architectures. ... Lemma 21 21 For*k*-*k*sorting*on*n × n*meshes*with M ≃ N*1*/2 ,T D2 (*k*, n) < T*route*(*k*, n) + O(n) + (6.5 + 17.1/ log*1*/2 N ) · √*k*· M + 2.5 · (*k*· log N · N/M )*1*/2For the values of N we consider, with ...##
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Optimal Many-to-One Routing on the Mesh with Constant Queues
[chapter]

2001
*
Lecture Notes in Computer Science
*

We present randomized and

doi:10.1007/3-540-44681-8_92
fatcat:2bw37sfxy5c5nk4byb5hnht2ei
*deterministic*algorithms for many-to-*one**routing**on*an n-node two-dimensional*mesh*under the store-and-forward model of packet*routing*. ... We consider the general instance of many-to-*one**routing*where each node is the source (resp., destination) of (resp.,*k*) packets, for arbitrary values of and*k*. ... We will develop randomized and*deterministic*algorithms for ( ,*k*)-*routing*for an n-node square*mesh*. ...##
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Optimal many-to-one routing on the mesh with constant queues

2005
*
Information Processing Letters
*

We present randomized and

doi:10.1016/j.ipl.2005.04.006
fatcat:ayoo4td5qvdrbcdo2bwyrw5svq
*deterministic*algorithms for many-to-*one**routing**on*an n-node two-dimensional*mesh*under the store-and-forward model of packet*routing*. ... We consider the general instance of many-to-*one**routing*where each node is the source (resp., destination) of (resp.,*k*) packets, for arbitrary values of and*k*. ... We will develop randomized and*deterministic*algorithms for ( ,*k*)-*routing*for an n-node square*mesh*. ...##
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Randomized Algorithms on the Mesh
[chapter]

1999
*
Combinatorial Optimization
*

In this paper, we survey the results

doi:10.1007/978-1-4613-3282-4_4
fatcat:nrvuh22a5neldjgysyftydy3ne
*on*three fundamental problems in parallel computation:*routing*, sorting, and selection, and demonstrate that randomized algorithms for these problems*on*the*mesh*are ... The*mesh*-connected array is an attractive architecture for parallel machines, and a number of existing parallel machines are based*on*a*mesh*topology. ... Randomized algorithms are also the best possible in several variants of the*routing*model such as cut-through*routing*34 ,*k*,*k**routing*34 , and de ection*routing*9,*1*7 , 3 0 , 14 . ...##
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Randomized algorithms on the mesh
[chapter]

1998
*
Lecture Notes in Computer Science
*

In this paper, we survey the results

doi:10.1007/3-540-64359-1_715
fatcat:5l453vvbzjhrpoyytuwn45dcbu
*on*three fundamental problems in parallel computation:*routing*, sorting, and selection, and demonstrate that randomized algorithms for these problems*on*the*mesh*are ... The*mesh*-connected array is an attractive architecture for parallel machines, and a number of existing parallel machines are based*on*a*mesh*topology. ... Randomized algorithms are also the best possible in several variants of the*routing*model such as cut-through*routing*34 ,*k*,*k**routing*34 , and de ection*routing*9,*1*7 , 3 0 , 14 . ...##
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A Recursive Deterministic Routing Algorithm for Two Dimensional Mesh Network

2021
*
International journal of computer science and mobile computing
*

Network performance in parallel systems, actually, depends

doi:10.47760/ijcsmc.2021.v10i03.001
fatcat:fywzx3b3lnbppeil6ie4qmbpvi
*on*network topology and the used*routing*algorithm.*Routing*can be classified as centralized, distributed,*deterministic*or adaptive. ... In this paper, we developed an optimal*deterministic*recursive*routing*algorithm for 2D*Mesh*network without wraparound link and enhanced it for 2D*Mesh*network with wraparound link (Torus). ...*Routing*can also be classified as*deterministic*or adaptive [2] . In*deterministic**routing*, a path that massage follows depends only*on*its source and destination nodes. ...##
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Flit-serial packet routing on meshes and tori

1996
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Mathematical Systems Theory
*

We present the first algorithms,

doi:10.1007/bf01192690
fatcat:e2z7w26qi5gnxdkduepmunu4oy
*deterministic*and probabitistic, based*on*this model for the permutation*routing*problem*on*a chain,*on*a square*mesh*, and*on*a square torus. 9 Cut-through model. ... In the cut-through with partial cuts*routing*model, for any snake s at time t, we have 0 _< collisions(s, t) <_*k*/2, i.e., we may have as many as*k*/2 collision points in snake s. ... Later, we use these results in the algorithm for the permutation*routing*problem*on*a square*mesh*. Problem*1*(Many-to-*One**Routing*). Initially, each processor has at most*one*packet to*route*. ...##
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Being Opportunistic or Being Concurrent -- On Designing Channel Assignment Algorithms in Multi-Radio, Multi-Channel Wireless Mesh Networks

2010
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2010 7th Annual IEEE Communications Society Conference on Sensor, Mesh and Ad Hoc Communications and Networks (SECON)
*

h (

doi:10.1109/secon.2010.5508210
dblp:conf/secon/WuRV10
fatcat:57ldbakstvcmffzkbu3lxbjdva
*1*−*k*j,h ) ⎞ ⎠ , (*1*) where Z*k*j is the workload of node j*on*channel*k*. ... is different from the traditional*deterministic**routing*techniques. ...##
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Application driven evaluation of network on chip architectures forcation parallel signal processing

2005
*
Advances in Radio Science
*

We focus

doi:10.5194/ars-2-181-2004
fatcat:tq5ustmoundzzaq666fu74njha
*on*the strictly orthogonal n-dimensional*mesh*, torus and*k*-ary-n cube networks comparing*deterministic*dimension-order and partially adaptive negative-first and planar-adaptive*routing*algorithms ... For each network topology and*routing*algorithm, input-and output-queued packet switching schemes are compared*on*the architectural level. ... This work has been supported by the Deutsche Forschungsgesellschaft (DFG) under grant We 2442/*1*-3 within the Schwerpunktprogramm "Grundlagen und Verfahren verlustarmer Informationsverarbeitung (VIVA)". ...
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