Isomorphism of degree four Cayley graph and wrapped butterfly and their optimal permutation routing algorithm

1999 ◽  
Vol 10 (12) ◽  
pp. 1290-1298 ◽  
Author(s):  
D.S.L. Wei ◽  
F.P. Muga ◽  
K. Naik
Keyword(s):  
Cayley Graph ◽  
Routing Algorithm ◽  
Optimal Permutation ◽  
Permutation Routing

scholarly journals An optimal permutation routing algorithm on full-duplex hexagonal networks

2008 ◽  
Vol Vol. 10 no. 3 (Distributed Computing and...) ◽  
Author(s):  
Ignasi Sau ◽  
Janez Žerovnik
Keyword(s):  
Distributed Computing ◽  
Routing Algorithm ◽  
Full Duplex ◽  
Triangular Grid ◽  
Translation Invariant ◽  
Routing Problem ◽  
Practical Applications ◽  
Optimal Permutation ◽  
International Audience ◽  
Permutation Routing

Distributed Computing and Networking International audience In the permutation routing problem, each processor is the origin of at most one packet and the destination of no more than one packet. The goal is to minimize the number of time steps required to route all packets to their respective destinations, under the constraint that each link can be crossed simultaneously by no more than one packet. We study this problem in a hexagonal network, i.e. a finite subgraph of a triangular grid, which is a widely used network in practical applications. We present an optimal distributed permutation routing algorithm on full-duplex hexagonal networks, using the addressing scheme described by F.G. Nocetti, I. Stojmenovic and J. Zhang (IEEE TPDS 13(9): 962-971, 2002). Furthermore, we prove that this algorithm is oblivious and translation invariant.

PERMUTATION ROUTING AND SORTING ON THE RECONFIGURABLE MESH

1998 ◽  
Vol 09 (02) ◽  
pp. 199-211
Author(s):  
SANGUTHEVAR RAJASEKARAN ◽  
THEODORE MCKENDALL
Keyword(s):  
Lower Bound ◽  
Randomized Algorithms ◽  
Linear Array ◽  
Order Term ◽  
Routing Algorithm ◽  
Sorting Algorithm ◽  
Routing Problem ◽  
Reconfigurable Mesh ◽  
Permutation Routing ◽  
Time Bounds

In this paper we demonstrate the power of reconfiguration by presenting efficient randomized algorithms for both packet routing and sorting on a reconfigurable mesh connected computer. The run times of these algorithms are better than the best achievable time bounds on a conventional mesh. Many variations of the reconfigurable mesh can be found in the literature. We define yet another variation which we call as Mr. We also make use of the standard PARBUS model. We show that permutation routing problem can be solved on a linear array Mr of size n in [Formula: see text] steps, whereas n-1 is the best possible run time without reconfiguration. A trivial lower bound for routing on Mr will be [Formula: see text]. On the PARBUS linear array, n is a lower bound and hence any standard n-step routing algorithm will be optimal. We also show that permutation routing on an n×n reconfigurable mesh Mr can be done in time n+o(n) using a randomized algorithm or in time 1.25n+o(n) deterministically. In contrast, 2n-2 is the diameter of a conventional mesh and hence routing and sorting will need at least 2n-2 steps on a conventional mesh. A lower bound of [Formula: see text] is in effect for routing on the 2D mesh Mr as well. On the other hand, n is a lower bound for routing on the PARBUS and our algorithms have the same time bounds on the PARBUS as well. Thus our randomized routing algorithm is optimal upto a lower order term. In addition we show that the problem of sorting can be solved in randomized time n+o(n) on Mr as well as on PARBUS. Clearly, this sorting algorithm will be optimal on the PARBUS model. The time bounds of our randomized algorithms hold with high probability.

A Permutation Routing Algorithm for Double Loop Networks

1997 ◽  
Vol 07 (03) ◽  
pp. 259-265 ◽  
Author(s):  
F. K. Hwang ◽  
Tzai-Shunne Lin ◽  
Rong-Hong Jan
Keyword(s):  
Parallel Processing ◽  
Routing Algorithm ◽  
Double Loop ◽  
Processing Capability ◽  
Permutation Routing ◽  
Double Loop Networks

Double-loop networks are popular architectures for interconnecting networks. We show that these networks have parallel processing capability by giving the first permutation routing algorithm. Furthermore, we show that the number of routing steps required is equal to the diameter of the network, the best bound one can get.

Optimal permutation routing for low-dimensional hypercubes

Networks ◽  
2009 ◽  
Vol 55 (2) ◽  
pp. 149-167
Author(s):  
Ambrose K. Laing ◽  
David W. Krumme
Keyword(s):  
Optimal Permutation ◽  
Low Dimensional ◽  
Permutation Routing

ON THE ROUTING NUMBER OF COMPLETE d-ARY TREES

2001 ◽  
Vol 12 (04) ◽  
pp. 411-434
Author(s):  
ALAN ROBERTS ◽  
ANTONIOS SYMVONIS
Keyword(s):  
Routing Algorithm ◽  
Permutation Routing

We consider the routing number of trees, denoted by rt(), with respect to the matching routing model. For an arbitrary n-node tree T, it is known that rt(T) < 3n/2 + O( log n). In this paper, by providing a recursive off-line permutation routing algorithm, we show that the routing number of an n-node complete d-ary tree of height h(T) > 1 is bounded from above by n + o(n). This is near optimal since, for an n-node complete d-ary tree T of height h(T) > 1 it holds that rt(T) ≥ n.

FAST, MINIMAL, AND OBLIVIOUS ROUTING ALGORITHMS ON THE MESH WITH BOUNDED QUEUES

2001 ◽  
Vol 02 (04) ◽  
pp. 445-469 ◽  
Author(s):  
AMI LITMAN ◽  
SHIRI MORAN-SCHEIN
Keyword(s):  
Queuing Theory ◽  
Routing Algorithm ◽  
Open Loop ◽  
Routing Algorithms ◽  
Routing Problem ◽  
Loop Control ◽  
Critical Edge ◽  
Oblivious Routing ◽  
Two Stages ◽  
Permutation Routing

This paper studies fast, deterministic permutation routing algorithms with bounded queues on the n×n mesh. Our main result is an O(n)-step, strongly-dimensional (and thus also source-oblivious and minimal) permutation routing algorithm. This algorithm works under a relaxed model in which nodes can freely send data to their neighbors. In a more prevalent model, the standard model, data may be sent only when accompanied by a packet. Under this model we present the following two algorithms: an O(n log n)-step strongly-dimensional algorithm and an O(n)-step oblivious and weakly-dimensional (and thus also minimal) algorithm. As said, all these algorithms store only O(1) packets in a node. Moreover, they use only O( log n) state bits in a node and transfer only O( log n) data bits on an edge in a step. All our routing algorithms are based on the following new technique of open-loop flow control. An algorithm is composed of two stages: setup and transportation. The setup stage computes certain values and stores them in the network. In particular, it computes a rational number α(e) for certain critical edges e. The transportation stage moves the packets to their destinations. It uses the computed values to slow the packets so that the traffic on each critical edge e is bounded byα(e); that is, at most ⌈α(e) · l⌉ packets traverse e during any l consecutive steps. This bounded on the burstiness of the traffic enables the algorithm to avoid hot spots and maintain bounded queues. The algorithm achieves this by an open-loop control; that is, during this stage no information is transferred in a direction opposite to that of the packets. An additional novelty of our algorithms is the application of a dynamic routing problem to solve a static one. The dynamic problem in question seems easy, as its networks is just a linear array. We show, however, that this problem is beyond the scope of the Adversarial Queuing Theory.

scholarly journals Least Common Ancestor Networks

VLSI Design ◽  
1995 ◽  
Vol 2 (4) ◽  
pp. 353-364 ◽  
Author(s):  
Isaac D. Scherson ◽  
Chi-Kai Chien
Keyword(s):  
Common Ancestor ◽  
Routing Algorithm ◽  
Routing Algorithms ◽  
Routing Strategy ◽  
Iterative Analysis ◽  
Simulation Results ◽  
Randomized Routing ◽  
Permutation Routing ◽  
Benes Networks

Least Common Ancestor Networks (LCANs) are introduced and shown to be a class of networks that include fattrees, baseline networks, SW-banyans and the router networks of the TRAC 1.1 and 2.0 and the CM-5. Some LCAN properties are stated and the circuit-switched permutation routing capabilities of an important subclass are analyzed. Simulation results for three permutation classes verify the accuracy of an iterative analysis for a randomized routing strategy. These results indicate that the routing strategy provides highly predictable router performance for all permutations. An off-line routing algorithm is also given, and it is shown how to realize certain classes of permutations by adapting Nassimi and Sahni's, and Raghavendra and Boppana's self-routing algorithms for Benes networks.

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