### Citations

1486 |
Introduction to Parallel Algorithms and Architectures,
- Leighton
- 1992
(Show Context)
Citation Context ...lization by Symvonis and Makedon in [14, 11]. The following two heuristic methods are based on the odd-even transposition method and the notion of normalization. 2 It is attributed to [2]. See [1] or =-=[9]-=- for a proof of correctness. 4s50 30 50 30 Figure 2: NO EXCHANGE 30 50 49 Figure 3: NORMALIZE 3.1.1 Complete Distance Normalization Heuristic The description of any routing algorithm must include two ... |

296 |
Universal schemes for parallel communicationâ€ť,
- Valiant, Brebner
- 1981
(Show Context)
Citation Context ...routing problem is important because it models the communication pattern that occurs in an EREW (Exclusive Read-Exclusive Write) PRAM. The rst algorithm was a probabilistic one by Valiant and Brebner =-=[15]-=-, later improved by Krizanc, Rajasekaran and Tsantilas [7]. Kunde [8] provided the rst deterministic algorithm that matched the results of the probabilistic ones. A major breakthrough was the algorith... |

207 |
The Design and Analysis of Parallel Algorithms.
- Akl
- 1989
(Show Context)
Citation Context ...e normalization by Symvonis and Makedon in [14, 11]. The following two heuristic methods are based on the odd-even transposition method and the notion of normalization. 2 It is attributed to [2]. See =-=[1]-=- or [9] for a proof of correctness. 4s50 30 50 30 Figure 2: NO EXCHANGE 30 50 49 Figure 3: NORMALIZE 3.1.1 Complete Distance Normalization Heuristic The description of any routing algorithm must inclu... |

41 |
Tsantilas, `Optimal Routing Algorithms for MeshConnected Processor Arrays
- Rajasekaran, Th
- 1992
(Show Context)
Citation Context ...ation pattern that occurs in an EREW (Exclusive Read-Exclusive Write) PRAM. The rst algorithm was a probabilistic one by Valiant and Brebner [15], later improved by Krizanc, Rajasekaran and Tsantilas =-=[7]-=-. Kunde [8] provided the rst deterministic algorithm that matched the results of the probabilistic ones. A major breakthrough was the algorithm by Makedon, Leighton and Tollis [10]. That algorithm was... |

36 | Constant Queue Routing on a Mesh",
- Rajasekaran, Overholt
- 1992
(Show Context)
Citation Context ...hton and Tollis [10]. That algorithm was time and space optimal and worked on two dimensional meshes. It performed the routing in optimal time using constant size queues of 1008 packets (according to =-=[12]-=-). Even though that result was a theoretical breakthrough, as the authors admit: \... it does not appear that the constant bound on the resulting queue size will be practical for moderate values of n.... |

32 | Derandomizing Algorithms for Routing and Sorting on Meshes - Kaufmann, Sibeyn, et al. - 1994 |

25 |
sorting on parallel models of computation
- Borodin, Hopcroft, et al.
- 1985
(Show Context)
Citation Context ...can transmit only one packet per communication link, some packets might have to be derouted. Despite the fact that this technique is very old (it was referenced as folklore by Borodin and Hopcroft in =-=[3]-=-) we are not able to make any statement regarding the number of routing steps that are required in the worst case in order to route any permutation. 3.2.1 Simple Randomization Heuristic It is obvious ... |

20 | Deterministic Permutation Routing on Meshes
- Chlebus, Kaufmann, et al.
- 1993
(Show Context)
Citation Context ...values of n." (n is the sidelength of the mesh.) That queue size was later reduced by Rajasekaran and Overholt [12] to about 150 packets (according to [13] 1 ). Later on, Chlebus, Kaufmann and Sibeyn =-=[4]-=- developed an optimal time (2n , 2 steps) algorithm which uses queues of at most 81 packets and a near optimal time (2n + O(1) steps) algorithm which uses a maximum queue of 31 packets. Subsequently, ... |

11 | Simple Path Selection for Optimal Routing on Processor Arrays - Kaklamanis, Krizanc, et al. - 1992 |

10 |
Electronic Data Sorting
- Demuth
- 1956
(Show Context)
Citation Context ...d distance normalization by Symvonis and Makedon in [14, 11]. The following two heuristic methods are based on the odd-even transposition method and the notion of normalization. 2 It is attributed to =-=[2]-=-. See [1] or [9] for a proof of correctness. 4s50 30 50 30 Figure 2: NO EXCHANGE 30 50 49 Figure 3: NORMALIZE 3.1.1 Complete Distance Normalization Heuristic The description of any routing algorithm m... |

7 | Shorter Queues for Permutation Routing on Meshes
- Sibeyn, Chlebus, et al.
- 1994
(Show Context)
Citation Context ...ulting queue size will be practical for moderate values of n." (n is the sidelength of the mesh.) That queue size was later reduced by Rajasekaran and Overholt [12] to about 150 packets (according to =-=[13]-=- 1 ). Later on, Chlebus, Kaufmann and Sibeyn [4] developed an optimal time (2n , 2 steps) algorithm which uses queues of at most 81 packets and a near optimal time (2n + O(1) steps) algorithm which us... |

6 |
Routing and Sorting on Mesh-Connected Arrays", VLSI Algorithms and Architectures
- Kunde
- 1988
(Show Context)
Citation Context ...rn that occurs in an EREW (Exclusive Read-Exclusive Write) PRAM. The rst algorithm was a probabilistic one by Valiant and Brebner [15], later improved by Krizanc, Rajasekaran and Tsantilas [7]. Kunde =-=[8]-=- provided the rst deterministic algorithm that matched the results of the probabilistic ones. A major breakthrough was the algorithm by Makedon, Leighton and Tollis [10]. That algorithm was time and s... |

4 |
A 2n-2 Algorithm for Routing in an n n Array With Constant Size Queues
- Leighton, Makedon, et al.
- 1989
(Show Context)
Citation Context ...ekaran and Tsantilas [7]. Kunde [8] provided the rst deterministic algorithm that matched the results of the probabilistic ones. A major breakthrough was the algorithm by Makedon, Leighton and Tollis =-=[10]-=-. That algorithm was time and space optimal and worked on two dimensional meshes. It performed the routing in optimal time using constant size queues of 1008 packets (according to [12]). Even though t... |

4 | An Efficient Heuristic for Permutation Packet Routing on Meshes with Low Buffer Requirements
- Makedon, Symvonis
- 1993
(Show Context)
Citation Context ...these algorithms still remain of pure theoretical interest since they are too complicated to be useful in an applied setting. A heuristic approach to the problem was presented by Symvonis and Makedon =-=[14, 11]-=-. Several classes of routing patterns were routed optimally while, for random permutations, the experimental behavior of the method was satisfactory. The paper is organized as follows: Section 2 conta... |

1 |
Packet Routing Problems on Mesh Connected Machines and High Resolution Layouts
- Symvonis
- 1991
(Show Context)
Citation Context ...these algorithms still remain of pure theoretical interest since they are too complicated to be useful in an applied setting. A heuristic approach to the problem was presented by Symvonis and Makedon =-=[14, 11]-=-. Several classes of routing patterns were routed optimally while, for random permutations, the experimental behavior of the method was satisfactory. The paper is organized as follows: Section 2 conta... |