## Routing and Sorting on Meshes with Row and Column Buses (1994)

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Citations: | 13 - 1 self |

### BibTeX

@MISC{Suel94routingand,

author = {Torsten Suel and V. K. Prasanna Kumar},

title = {Routing and Sorting on Meshes with Row and Column Buses},

year = {1994}

}

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### Abstract

of the 27th Annual IEEE Symposium on Foundations of Computer Science, pages 264--273, 1986. [50] T. Suel. Routing and sorting on meshes with row and column buses. In Proceedings of the 8th International Parallel Processing Symposium, April 1994. [51] B. Wang and G. Chen. Constant time algorithms for the transitive closure and some related graph problems on processor arrays with reconfigurable bus systems. IEEE Transactions on Parallel and Distributed Systems, 1:500--507, 1990. [27] M. Kunde. Block gossiping on grids and tori: Deterministic sorting and routing match the bisection bound. In Proceedings of the 1st Annual European Symposium on Algorithms, September 1993. [28] R. E. Ladner, J. Lampe, and R. Rogers. Vector prefix addition on sub-bus mesh computers. In Proceedings of the 5th Annual ACM Symposium on Parallel Algorithms and Architectures, pages 387--396, June 1993. [29] F. T. Leighton. Tight bounds on the com

### Citations

1308 |
Introduction to Parallel Algorithms and Architectures: Arrays
- Leighton
- 1992
(Show Context)
Citation Context ...ively studied problems are those of routing and sorting. The main drawback of the mesh is its large diameter in comparison to many other networks, such as the mesh of trees or the hypercubic networks =-=[10]-=-. An n \Theta n mesh has a diameter of 2n \Gamma 2, and hence even computations that require only a very limited amount of communication, for example prefix computations, require at least n \Gamma 1 c... |

544 |
An n5/2 algorithm for maximum matchings in bipartite graphs
- Hopcroft, Karp
- 1973
(Show Context)
Citation Context ...ching the length of the schedule is increased by at least one step. A maximum matching on a bipartite graph with 2n vertices can be computed in time O(n 2:5 ) using the algorithm of Hopcroft and Karp =-=[6]-=-. Thus, the entire schedule can be computed in time O(n 3:5 ). Of course, this makes the algorithm inappropriate for use as an on-line algorithm. 2.2 Two-Dimensional Routing In order to get a running ... |

167 | Tight bounds on the complexity of parallel sorting - Leighton - 1985 |

94 | Openshop Scheduling to Minimize Finish Time
- Gonzdez, Sahni
- 1976
(Show Context)
Citation Context ...rocess uses at most one resource. The problem of finding a minimum time schedule that satisfies all of these demands is known as the Open Shop Scheduling Problem, and was solved by Gonzalez and Sahni =-=[5]-=-. For 0si; j ! n, let D i;j , the demand of process P i for resource R j , be the number of packets in column i that have a destination in row j. Note that n\Gamma1 X i=0 D i;j = n and n\Gamma1 X j=0 ... |

87 | An Optimal Sorting Algorithm for Mesh Connected Computers - Schnorr, Shamir - 1986 |

85 | The Power of Reconfiguration - Ben-Asher - 1991 |

61 |
Parallel computations on reconfigurable meshes
- Miller, Prasanna-Kumar, et al.
- 1993
(Show Context)
Citation Context ...se models. Among the most frequently studied problems on meshes with buses are Maximum, Prefix Sums, Selection, as well as various algorithmic problems in image processing and graph theory (e.g., see =-=[13, 14, 20]-=- for a list of references). Due to the low communication requirements of these problems, significant speed-ups over the standard mesh can be achieved. The exact time complexities of the proposed algor... |

57 | Constant time algorithms for the transitive closure and some related graph problems on processor arrays with reconfigurable bus systems - Wang, Chen - 1990 |

53 | A fast parallel algorithm for routing in permutation networks - Lev, Pippenger, et al. - 1981 |

46 |
Efficient optical communication in parallel computers
- Gerèb-Graus, Tsantilas
- 1992
(Show Context)
Citation Context ...a(lg n lg lg n) packets will be generated in each row. To route these packets across the row buses to their destination column, we can use an algorithm recently analyzed by Ger'eb-Graus and Tsantilas =-=[4]-=- in the context of routing h-relations on an optical computer model. The algorithm uses appropriately biased coin-flips to route O(lg n lg lg n) packets in time O(lg n lg lg n), with high probability.... |

42 | Array Processor with Multiple Broadcasting - Kumar, Raghavendra - 1987 |

40 |
Finding Maximum on an Array Processor with a Global Bus
- Bokhari
- 1984
(Show Context)
Citation Context ...hat require only a very limited amount of communication, for example prefix computations, require at least n \Gamma 1 communication steps. To remedy this situation, it was proposed by several authors =-=[2, 7, 19]-=- to augment the mesh architecture with highspeed buses that allow fast communication between processors located in different areas of the mesh. This has resulted in a large body of literature on vario... |

38 |
Tsitsiklis. The efficiency of greedy routing in hypercubes and butterflies
- Stamoulis, N
- 1991
(Show Context)
Citation Context ...re randomly chosen among the processors of the network. While dynamic routing problems have been studied on several other classes of networks, including the mesh [10, Section 1.7.2] and the hypercube =-=[18]-=-, we are not aware of any previous attempt to analyze the performance of meshes with buses on these problems. In the case of permutation routing and sorting, it is easy to see that at least \Theta(n) ... |

36 | A Fast Algorithm for Computing Histograms on a Reconfigurable Mesh - Jang, Park, et al. - 1992 |

35 | Matching the bisection bound for routing and sorting on the mesh - Kaufmann, Rajasekaran, et al. - 1992 |

34 | gossiping on grids and tori: Deterministic sorting and routing match the bisection bound - Kunde, “Block - 1991 |

32 | Square Meshes are not always Optimal - Bar-Noy, Peleg - 1991 |

30 | Derandomizing Algorithms for Routing and Sorting on Meshes
- Kaufmann, Torsten, et al.
- 1994
(Show Context)
Citation Context ...bound. An optimal deterministic algorithm for k--k sorting on the mesh with reconfigurable buses can be obtained by a straightforward implementation of the optimal algorithms for the standard mesh in =-=[8, 9]-=-. 1.2 Overview of the Paper In this paper, we study the complexity of permutation routing, sorting, and dynamic routing on meshes with fixed and reconfigurable row and column buses. We give a fairly s... |

30 | Optimal bounds for finding maximum on array of processors with k global buses - Aggarwal - 1986 |

27 | Designing Efficient Parallel Algorithms on MeshConnected Computers with Multiple Broadcasting - Chen, Chen, et al. - 1990 |

25 |
Reconfigurable Massively Parallel Computers
- Li, Stout, et al.
- 1991
(Show Context)
Citation Context ...se models. Among the most frequently studied problems on meshes with buses are Maximum, Prefix Sums, Selection, as well as various algorithmic problems in image processing and graph theory (e.g., see =-=[13, 14, 20]-=- for a list of references). Due to the low communication requirements of these problems, significant speed-ups over the standard mesh can be achieved. The exact time complexities of the proposed algor... |

25 | Mesh connected computers with fixed and reconfigurable buses: packet routing, sorting and selection
- Rajasekaran
- 1993
(Show Context)
Citation Context ... In a subsequent paper [12], they obtain an improved algorithm for the two-dimensional case, running in time (1 + ffl)n + o(n) with queue size O(1=ffl). Rajasekaran and McKendall [16] and Rajasekaran =-=[15]-=- describe randomized algorithm for routing and sorting on a mesh in which the mesh edges have been replaced by a reconfigurable bus system. This model, hereafter referred to as the mesh with reconfigu... |

24 |
A special purpose architecture for finite element analysis
- JORDAN
(Show Context)
Citation Context ...hat require only a very limited amount of communication, for example prefix computations, require at least n \Gamma 1 communication steps. To remedy this situation, it was proposed by several authors =-=[2, 7, 19]-=- to augment the mesh architecture with highspeed buses that allow fast communication between processors located in different areas of the mesh. This has resulted in a large body of literature on vario... |

23 | Meshes with multiple buses - Stout - 1986 |

20 |
Mesh-Connected Computers with Broadcasting
- Stout
- 1983
(Show Context)
Citation Context ...hat require only a very limited amount of communication, for example prefix computations, require at least n \Gamma 1 communication steps. To remedy this situation, it was proposed by several authors =-=[2, 7, 19]-=- to augment the mesh architecture with highspeed buses that allow fast communication between processors located in different areas of the mesh. This has resulted in a large body of literature on vario... |

17 | Array processors with pipelined optical busses - Guo, Melhem, et al. - 1991 |

16 | Efficient median finding and its application to two-variable linear programming on mesh connected computers with multiple broadcasting - Chen, Chen - 1992 |

15 |
A unified approach to off-line permutation routing on parallel networks
- Annexstein, Baumslag
- 1990
(Show Context)
Citation Context ... [20]. Moreover, our algorithm achieves a queue size of 2. In this context, we point out that the 3n \Gamma 3 step offline scheme for routing on the standard mesh described by Annexstein and Baumslag =-=[1]-=- achieves a queue size of 1 only because in the standard mesh model two packets can be exchanged across an edge in a single step. Since we do not allow two arbitrary processors that are connected to a... |

14 | Selection on the reconfigurable mesh - Hao, MacKenzie, et al. - 1992 |

12 |
gossiping on grids and tori: Deterministic sorting and routing match the bisection bound
- Block
- 1993
(Show Context)
Citation Context ...bound. An optimal deterministic algorithm for k--k sorting on the mesh with reconfigurable buses can be obtained by a straightforward implementation of the optimal algorithms for the standard mesh in =-=[8, 9]-=-. 1.2 Overview of the Paper In this paper, we study the complexity of permutation routing, sorting, and dynamic routing on meshes with fixed and reconfigurable row and column buses. We give a fairly s... |

12 | A parallel median algorithm - Cole, Yap - 1985 |

10 |
Packet routing on square meshes with row and column buses
- Leung, Shende
- 1991
(Show Context)
Citation Context ...tion width. However, the exact complexity of these problems has only recently been investigated. The study of permutation routing on meshes with row and column buses was initiated by Leung and Shende =-=[11]-=-. They assume a model of computation, hereafter referred to as the mesh with fixed buses, that consists of a mesh with nonreconfigurable row and column buses in addition to the standard mesh edges. Fo... |

9 | Permutation routing and sorting on the reconfigurable mesh
- Rajasekaran, McKendall
- 1992
(Show Context)
Citation Context ...dimensional networks. In a subsequent paper [12], they obtain an improved algorithm for the two-dimensional case, running in time (1 + ffl)n + o(n) with queue size O(1=ffl). Rajasekaran and McKendall =-=[16]-=- and Rajasekaran [15] describe randomized algorithm for routing and sorting on a mesh in which the mesh edges have been replaced by a reconfigurable bus system. This model, hereafter referred to as th... |

9 | Randomized routing on meshes with buses, in
- Sibeyn, Kaufmann, et al.
- 1993
(Show Context)
Citation Context ...and a queue size of O(1=ffl), with high probability. They also obtain randomized algorithms for sorting with the same bounds on running time and queue size. Very recently, Sibeyn, Kaufmann, and Raman =-=[17]-=- have shown improved lower bounds for routing on the d-dimensional mesh with fixed buses. In particular, they obtain lower bounds of 0:69n and 0:72n for the two-dimensional and threedimensional case, ... |

9 | Permutation Routing on Reconfigurable Meshes - Cogolludo, Rajasekaran - 2001 |

7 | On multidimensional packet routing for meshes with buses - Leung, Shende - 1994 |

6 | On the performance of networks with multiple busses, in - Heide, Pham - 1992 |

4 |
A lower bound for permutation routing on two-dimensional bused meshes
- Cheung, Lau
- 1993
(Show Context)
Citation Context ...nd threedimensional case, respectively. For large d, their lower bounds are approximately d\Gamma1 d n. The lower bound for the twodimensional case was also independently discovered by Cheung and Lau =-=[3]-=-. Sibeyn, Kaufmann, and Raman also give randomized algorithms for permutation routing on meshes with fixed buses that are significantly faster than the deterministic algorithms of Leung and Shende. Fo... |

4 | Complexity of sub-bus mesh computations - Condon, Ladner, et al. - 1993 |

3 | Image processing on enhanced mesh connected computers - Kumar, Raghavendra - 1985 |

3 | Packed exponential connections - a hierarchy of 2-D meshes - Kirkman, Quammen - 1991 |

3 | Routing problems on the mesh of buses - Iwama, Miyano, et al. - 1992 |

2 | Vector prefix addition on sub-bus mesh computers - Ladner, Lampe, et al. - 1993 |

2 | An O(lg n) parallel connectivity algorithm on the mesh - Iwama, Kambayashi - 1989 |