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.

(ℓ, k)-ROUTING ON PLANE GRIDS

2009 ◽  
Vol 10 (01n02) ◽  
pp. 27-57
Author(s):  
FLORIAN HUC ◽  
IGNASI SAU ◽  
JANEZ ŽEROVNIK
Keyword(s):  
Communication Networks ◽  
Routing Algorithms ◽  
Full Duplex ◽  
Packet Routing ◽  
Routing Problem ◽  
Shortest Path Routing ◽  
Running Time ◽  
Half Duplex ◽  
Hexagonal Grids ◽  
Permutation Routing

The packet routing problem plays an essential role in communication networks. It involves how to transfer data from some origins to some destinations within a reasonable amount of time. In the (ℓ, k)-routing problem, each node can send at most ℓ packets and receive at most k packets. Permutation routing is the particular case ℓ = k = 1. In the r-central routing problem, all nodes at distance at most r from a fixed node v want to send a packet to v. In this article we study the permutation routing, the r-central routing and the general (ℓ, k)-routing problems on plane grids, that is square grids, triangular grids and hexagonal grids. We use the store-and-forward Δ-port model, and we consider both full and half-duplex networks. We first survey the existing results in the literature about packet routing, with special emphasis on (ℓ, k)-routing on plane grids. Our main contributions are the following: 1. Tight permutation routing algorithms on full-duplex hexagonal grids, and half duplex triangular and hexagonal grids. 2. Tight r-central routing algorithms on triangular and hexagonal grids. 3. Tight (k, k)-routing algorithms on square, triangular and hexagonal grids. 4. Good approximation algorithms (in terms of running time) for (ℓ, k)-routing on square, triangular and hexagonal grids, together with new lower bounds on the running time of any algorithm using shortest path routing. These algorithms are all completely distributed, i.e., can be implemented independently at each node. Finally, we also formulate the (ℓ, k)-routing problem as a WEIGHTED EDGE COLORING problem on bipartite graphs.

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.

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

A COMPARISON OF MESHES WITH STATIC BUSES AND HALF-DUPLEX WRAP-AROUNDS

1993 ◽  
Vol 03 (02) ◽  
pp. 109-114 ◽  
Author(s):  
DANNY KRIZANC ◽  
SANGUTHEVAR RAJASEKARAN ◽  
SUNIL M. SHENDE
Keyword(s):  
High Probability ◽  
Linear Array ◽  
Routing Algorithm ◽  
Two Dimensional ◽  
Routing Problem ◽  
Half Duplex ◽  
Run Time ◽  
Clock Tick ◽  
Permutation Routing

We investigate the relative computational powers of a mesh with static buses and a mesh with half-duplex wrap-arounds. The latter model is like a torus, except that any wrap-around link of the architecture can only transmit data in one of the two directions at any clock tick. We show that the permutation routing problem can be solved as efficiently on a linear array augmented with a half-duplex wrap-around link, as on a linear array with an augmented broadcast bus. We also present a routing algorithm for a two-dimensional (2D) mesh with half-duplex wrap-around links whose run time is close to that of the best known algorithm for routing on a 2D mesh with broadcast buses in each dimension. In addition, we show that on an n×n 2D mesh with broadcast buses, randomized sorting of n2 elements can be accomplished in time that is only o(n) more, with high probability, than the time needed for permutation routing.

scholarly journals An Optimum Channel Routing Algorithm in the Knock-knee Diagonal Model

VLSI Design ◽  
1994 ◽  
Vol 1 (3) ◽  
pp. 233-242 ◽  
Author(s):  
Xiaoyu Song
Keyword(s):  
Routing Algorithm ◽  
Difficult Problem ◽  
Layout Design ◽  
Channel Routing ◽  
Routing Problem ◽  
Vlsi Layout ◽  
Channel Density ◽  
Optimum Algorithm ◽  
Important Time ◽  
Optimum Channel

Channel routing problem is an important, time consuming and difficult problem in VLSI layout design. In this paper, we consider the two-terminal channel routing problem in a new routing model, called knock-knee diagonal model, where the grid consists of right and left tracks displayed at +45° and –45°. An optimum algorithm is presented, which obtains d + 1 as an upper bound to the channel width, where d is the channel density.

Multicast Routing Algorithm with QoS Constraints in Mobile Ad Hoc Networks

2014 ◽  
Vol 602-605 ◽  
pp. 3169-3172 ◽  
Author(s):  
Yue Li ◽  
Yin Hui Liu ◽  
Zhong Bao Luo
Keyword(s):  
Ad Hoc ◽  
Multicast Routing ◽  
Routing Algorithm ◽  
Estimation Algorithm ◽  
Bandwidth Estimation ◽  
Routing Problem ◽  
Network Bandwidth ◽  
Hoc Networks ◽  
Multicast Routing Algorithm ◽  
Select Function

Through the study of MANET's QoS multicast routing problem, we propose a heuristic-demand multicast routing algorithm. Algorithm combines the MANET network bandwidth estimation algorithm, redefined the select function, restrictions request packets of flooding algorithm, to ensure fair treatment delay and bandwidth. Simulation results show that the algorithm has the advantage of fewer routing overhead, high success rate.

scholarly journals Stochastic Flips on Dimer Tilings

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Thomas Fernique ◽  
Damien Regnault
Keyword(s):  
Fixed Point ◽  
Markov Process ◽  
Upper Bound ◽  
Numerical Experiments ◽  
Triangular Grid ◽  
Expected Number ◽  
Worst Case ◽  
Average Case ◽  
International Audience

International audience This paper introduces a Markov process inspired by the problem of quasicrystal growth. It acts over dimer tilings of the triangular grid by randomly performing local transformations, called $\textit{flips}$, which do not increase the number of identical adjacent tiles (this number can be thought as the tiling energy). Fixed-points of such a process play the role of quasicrystals. We are here interested in the worst-case expected number of flips to converge towards a fixed-point. Numerical experiments suggest a $\Theta (n^2)$ bound, where $n$ is the number of tiles of the tiling. We prove a $O(n^{2.5})$ upper bound and discuss the gap between this bound and the previous one. We also briefly discuss the average-case.

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.

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