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Proceedings ArticleDOI

Protection mechanism for the N2R topological routing algorithm

15 May 2008-pp 170-176

TL;DR: Protection against failures is introduced by modifying the previous algorithm implementing the option of routing a packet using a second independent path, proving that there is an easy and efficient method to route topologically a packet (in case of a failure) using an alternative path with no record at all.

AbstractThe topological routing over N2R structures has previously been studied and implemented using different techniques. A first approach was achieved obtaining the best trade off between path length vs. path completion time for the shortest path between any pair of nodes. This paper introduces protection against failures by modifying the previous algorithm implementing the option of routing a packet using a second independent path. The goal is to prove that there is an easy and efficient method to route topologically a packet (in case of a failure) using an alternative path with no record at all of the original.

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Citations
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Proceedings ArticleDOI
13 Apr 2008
TL;DR: The goal is to prove that there is an easy and efficient method for restoration in case of a failure of any element, when failures occurs, being able to reroute the packets to the destination when the main path is not available.
Abstract: The topological routing over N2R structures has been studied and implemented using different techniques. An implemented algorithm achieves good performance and a restoration mechanism has been added to the algorithm to obtain higher reliability. This paper introduces the concept of restoration, when failures occurs, being able to reroute the packets to the destination when the main path is not available. The goal is prove that there is an easy and efficient method for restoration in case of a failure of any element.

3 citations


Cites background or methods from "Protection mechanism for the N2R to..."

  • ...The nodes are degree three, hence, if there are three neighbor elements failing at the same time, the node is isolated, and there is no need for three entries in the table....

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  • ...To avoid forming two separated networks in the inner ring, q must fulfil gcd(p, q) = 1 (Greatest Common Divisor), also q is evaluated from 1 to p/2 [2]....

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  • ...The solution proposed in this paper for a reliable topological routing is based on this algorithm....

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Journal ArticleDOI
TL;DR: The network plan presented in the paper contains both topological structure of fiber optic network as well as the active equipment for the network, which provides low cost of construction, ease of implementation of the network and low operating cost.
Abstract: Abstract In the paper the designing project (plan) of Tuchola City broadband IP optical network has been presented. The extended version of network plan constitute technical part of network Feasibility Study, that it is expected to be implemented in Tuchola and be financed from European Regional Development Funds. The network plan presented in the paper contains both topological structure of fiber optic network as well as the active equipment for the network. In the project described in the paper it has been suggested to use Modular Cable System - MCS for passive infrastructure and Metro Ethernet technology for active equipment. The presented solution provides low cost of construction (CAPEX), ease of implementation of the network and low operating cost (OPEX). Moreover the parameters of installed Metro Ethernet switches in the network guarantee the scalability of the network for at least 10 years.

2 citations



Journal ArticleDOI
TL;DR: This paper gives an overview of the work done, and provides appropriate references to the work for further details, as a tribute to Professor and Dean Antoni Zabłudowski who passed away during 2012.
Abstract: Abstract In this short paper we summarize the main results of 10 years of research on network topologies carried out jointly at Aalborg University (AAU), Aalborg, Denmark, and University of Life Science (UTP), Bydgoszcz, Poland. The starting points are the Chordal Rings, which were mainly studied in UTP, and the N2R which were studied at AAU. From here the universities have collaborated intensely, and studied a number of alternatives and variations of the original topologies, based on methodologies developed both independently and jointly over time. This paper gives an overview of the work done, and provides appropriate references to the work for further details. The paper is presented as a tribute to Professor and Dean Antoni Zabłudowski who passed away during 2012.

1 citations


Cites background from "Protection mechanism for the N2R to..."

  • ...In addition to the ongoing work on distances, a good amount of research in Aalborg was dealing with reliability in N2R networks, specifically on protection and restoration mechanisms [32] [33]....

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References
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Journal ArticleDOI
04 Jun 1998-Nature
TL;DR: Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.
Abstract: Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.

35,972 citations


"Protection mechanism for the N2R to..." refers methods in this paper

  • ...Kleinberg’s Small-world models [2] or the Watts and Strogatz Ring Model [3] are examples of the extensive literature which prove the existence of topological routing algorithms....

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Journal ArticleDOI
TL;DR: The honeycomb mesh, based on hexagonal plane tessellation, is considered as a multiprocessor interconnection network and honeycomb networks with rhombus and rectangle as the bounding polygons are considered.
Abstract: The honeycomb mesh, based on hexagonal plane tessellation, is considered as a multiprocessor interconnection network. A honeycomb mesh network with n nodes has degree 3 and diameter /spl ap/1.63/spl radic/n-1, which is 25 percent smaller degree and 18.5 percent smaller diameter than the mesh-connected computer with approximately the same number of nodes. Vertex and edge symmetric honeycomb torus network is obtained by adding wraparound edges to the honeycomb mesh. The network cost, defined as the product of degree and diameter, is better for honeycomb networks than for the two other families based on square (mesh-connected computers and tori) and triangular (hexagonal meshes and tori) tessellations. A convenient addressing scheme for nodes is introduced which provides simple computation of shortest paths and the diameter. Simple and optimal (in the number of required communication steps) routing, broadcasting, and semigroup computation algorithms are developed. The average distance in honeycomb torus with n nodes is proved to be approximately 0.54/spl radic/n. In addition to honeycomb meshes bounded by a regular hexagon, we consider also honeycomb networks with rhombus and rectangle as the bounding polygons.

279 citations


Journal ArticleDOI
TL;DR: A deterministic fault-tolerant and deadlock-free routing protocol in two-dimensional meshes based on dimension-order routing and the odd-even turn model is proposed, called extended X-Y routing.
Abstract: We propose a deterministic fault-tolerant and deadlock-free routing protocol in two-dimensional (2D) meshes based on dimension-order routing and the odd-even turn model. The proposed protocol, called extended X-Y routing, does not use any virtual channels by prohibiting certain locations of faults and destinations. Faults are contained in a set of disjointed rectangular regions called faulty blocks. The number of faults to be tolerated is unbounded as long as nodes outside faulty blocks are connected in the 2D mesh network. The extended X-Y routing can also be used under a special convex fault region called an orthogonal faulty block, which can be derived from a given faulty block by activating some nonfaulty nodes in the block. Extensions to partially adaptive routing, traffic and adaptivity-balancing using virtual networks, and routing without constraints using virtual channels and virtual networks are also discussed.

221 citations


"Protection mechanism for the N2R to..." refers background in this paper

  • ...be considered This improvement will give a protection against failures which will make the topological routing more feasible over N2R structures [12]....

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Journal ArticleDOI
01 Sep 1971
Abstract: 1. Introduction. For integers n and k with 2 ≤ 2k < n, the generalized Petersen graph G(n, k) has been defined in (8) to have vertex-setand edge-set E(G(n, k)) to consist of all edges of the formwhere i is an integer. All subscripts in this paper are to be read modulo n, where the particular value of n will be clear from the context. Thus G(n, k) is always a trivalent graph of order 2n, and G(5, 2) is the well known Petersen graph. (The subclass of these graphs with n and k relatively prime was first considered by Coxeter ((2), p. 417ff.).)

179 citations


"Protection mechanism for the N2R to..." refers background in this paper

  • ...These structures, which are a subset of Petersen graphs [8], offer better properties than other degree 3 topologies such as Double Rings [9] or Degree Three Chordal Rings [10] and [11] in terms of average distances between any pair of nodes or diameters of the network....

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Proceedings ArticleDOI
25 Jul 2004
TL;DR: The properties of Small-World networks, where links are much more likely to connect "neighbor nodes" than distant nodes, are analyzed, and expected θ(log n) diameter results for higher dimensional grids, as well as settings with less uniform base structures.
Abstract: We analyze the properties of Small-World networks, where links are much more likely to connect "neighbor nodes" than distant nodes. In particular, our analysis provides new results for Kleinberg's Small-World model and its extensions. Kleinberg adds a number of directed long-range random links to an nxn lattice network (vertices as nodes of a grid, undirected edges between any two adjacent nodes). Links have a non-uniform distribution that favors arcs to close nodes over more distant ones. He shows that the following phenomenon occurs: between any two nodes a path with expected length O(log2n) can be found using a simple greedy algorithm which has no global knowledge of long-range links.We show that Kleinberg's analysis is tight: his algorithm achieves θ(log2n) delivery time. Moreover, we show that the expected diameter of the graph is θlog n), a log n factor smaller. We also extend our results to the general k-dimensional model. Our diameter results extend traditional work on the diameter of random graphs which largely focuses on uniformly distributed arcs. Using a little additional knowledge of the graph, we show that we can find shorter paths: with expected length O(log3/2n) in the basic 2-dimensional model and O(log1+1/k) in the general k-dimensional model (fork≥1).Finally, we suggest a general approach to analyzing a broader class of random graphs with non-uniform edge probabilities. Thus we show expected θ(log n) diameter results for higher dimensional grids, as well as settings with less uniform base structures: where links can be missing, where the probability can vary at different nodes, or where grid-related factors (e.g. the use of lattice distance) has a weaker role or is dismissed, and constraints (such as the uniformness of degree distribution) are relaxed.

153 citations


"Protection mechanism for the N2R to..." refers methods in this paper

  • ...Kleinberg's Small-world models [ 2 ] or the Watts and Strogatz Ring Model [3] are examples of the extensive literature which prove the existence of topological routing algorithms....

    [...]