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

Jop F. Sibeyn, Michael Kaufmann
1994 Lecture Notes in Computer Science  
Non-trivial extensions are given to the general l-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.  ... 
doi:10.1007/3-540-57785-8_145 fatcat:apson42lwrdh3emzkgmgszi4yi

Block gossiping on grids and tori: Deterministic sorting and routing match the bisection bound [chapter]

Manfred Kunde
1993 Lecture Notes in Computer Science  
This proves that all packets reach their destination row in time under distribution 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.  ... 
doi:10.1007/3-540-57273-2_62 fatcat:i6er5xsf6vc4fhtynlc6eeuomi

Deterministic Routing with HoL-Blocking-Awareness for Direct Topologies

R. Peñaranda, C. Gómez, M.E. Gómez, P. López, J. Duato
2013 Procedia Computer Science  
Depending 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.  ...  k1 (i.e., nodes are numbered from 0, 0, ..., 0 to k1, k1, ..., k1 ).  ... 
doi:10.1016/j.procs.2013.05.432 fatcat:2thnl7urmjgmhf42gvqpv26yiu

Analysis of minimal path routing schemes in the presence of faults

Jesse M. Gordon
1992 Discrete Applied Mathematics  
Using this framework, we derive closed form solutions for a wide range of 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.  ... 
doi:10.1016/0166-218x(92)90136-x fatcat:gmcyecripfdorfrm3fmlobyfwi

Faster deterministic sorting through better sampling

Jop F. Sibeyn
2003 Theoretical Computer Science  
The method is illustrated by a detailed analysis for the cases of sorting 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  ... 
doi:10.1016/s0304-3975(02)00321-3 fatcat:2rfn4jbj2zdznl6xoqpax6yakq

Improved bounds for routing and sorting on multi-dimensional meshes

Torsten Suel
1994 Proceedings of the sixth annual ACM symposium on Parallel algorithms and architectures - SPAA '94  
We show improved bounds for 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.  ... 
doi:10.1145/181014.181022 dblp:conf/spaa/Suel94 fatcat:gzpamh3z5nec3bpx6zkx7lsnki

Sample sort on meshes [chapter]

Jop F. Sibeyn
1997 Lecture Notes in Computer Science  
We come with a new 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  ... 
doi:10.1007/bfb0002762 fatcat:jqaknhy7rjeqxckoupikkxpouu

Optimal Many-to-One Routing on the Mesh with Constant Queues [chapter]

Andrea Pietracaprina, Geppino Pucci
2001 Lecture Notes in Computer Science  
We present randomized and 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.  ... 
doi:10.1007/3-540-44681-8_92 fatcat:2bw37sfxy5c5nk4byb5hnht2ei

Optimal many-to-one routing on the mesh with constant queues

Andrea Pietracaprina, Geppino Pucci
2005 Information Processing Letters  
We present randomized and 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.  ... 
doi:10.1016/j.ipl.2005.04.006 fatcat:ayoo4td5qvdrbcdo2bwyrw5svq

Randomized Algorithms on the Mesh [chapter]

Lata Narayanan
1999 Combinatorial Optimization  
In this paper, we survey the results 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 .  ... 
doi:10.1007/978-1-4613-3282-4_4 fatcat:nrvuh22a5neldjgysyftydy3ne

Randomized algorithms on the mesh [chapter]

Lata Narayanan
1998 Lecture Notes in Computer Science  
In this paper, we survey the results 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 .  ... 
doi:10.1007/3-540-64359-1_715 fatcat:5l453vvbzjhrpoyytuwn45dcbu

A Recursive Deterministic Routing Algorithm for Two Dimensional Mesh Network

Abdulelah G.F. Saif
2021 International journal of computer science and mobile computing  
Network performance in parallel systems, actually, depends 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.  ... 
doi:10.47760/ijcsmc.2021.v10i03.001 fatcat:fywzx3b3lnbppeil6ie4qmbpvi

Flit-serial packet routing on meshes and tori

F. Makedon, A. Symvonis
1996 Mathematical Systems Theory  
We present the first algorithms, 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.  ... 
doi:10.1007/bf01192690 fatcat:e2z7w26qi5gnxdkduepmunu4oy

Being Opportunistic or Being Concurrent -- On Designing Channel Assignment Algorithms in Multi-Radio, Multi-Channel Wireless Mesh Networks

Fan Wu, Vijay Raman, Nitin Vaidya
2010 2010 7th Annual IEEE Communications Society Conference on Sensor, Mesh and Ad Hoc Communications and Networks (SECON)  
h (1k j,h ) ⎞ ⎠ , (1) where Z k j is the workload of node j on channel k.  ...  is different from the traditional deterministic routing techniques.  ... 
doi:10.1109/secon.2010.5508210 dblp:conf/secon/WuRV10 fatcat:57ldbakstvcmffzkbu3lxbjdva

Application driven evaluation of network on chip architectures forcation parallel signal processing

C. Neeb, M. J. Thul, N. Wehn
2005 Advances in Radio Science  
We focus 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)".  ... 
doi:10.5194/ars-2-181-2004 fatcat:tq5ustmoundzzaq666fu74njha
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