Boolean Routing on High Degree Chordal Ring Networks

Over the past twenty-five years, the telecommunication field has evolved rapidly. Telephone and computer networks, now nearly ubiquitous, provide access to voice, data and video services throughout the world. As networking technologies evolve and proliferate, researchers develop new traffic routing strategies. The problem of routing in a distributed system has been investigated and issues concerning Boolean routing schemes have been considered. All compact routing techniques minimise time and space complexity. A good routing algorithm optimises the time and space complexity and a routing algorithm that has O(1) time complexity and O(log n) space complexity for high degree chordal ring has been found. A Boolean Routing Scheme (BRS) has been applied on ring topology and regular chordal ring of degree three. It was found that the regular chordal ring of degree three can be represented geometrically. the regular chordal ring of degree three has been categorised into two categories; the first is the regular chordal ring of degree three that satisfies the following formula n mod 4 = 0 and the second other is n mod 4≠0, where n is the number of nodes that the graph contains. A BRS that requires O(log n) bits of storage at each node, O(1) time complexity to compute a shortest path to any destination for the regular chordal ring of degree three and Ө(log n) bits of storage at each node. O(1) time complexity to compute a shortest path to any destination for the ring topologies has been shown. The BRS has been applied on chordal ring of degree six. it has been found that the chordal ring of degree six can be represented geometrically and the representation would be in three dimensions (in the space). Very little is known about routing on high degree chordal rings. A BRS that requires O(log n) bits of storage at each node ,and 0(1) time complexity to compute a shortest path to any destination for the chordal ring of degree six topologyhas been shown. The chordal ring 0(27;9;3) has been considered as a case to apply BRS

Gossiping in chordal rings under the line model

The line model assumes long distance calls between non neighboring processors. In this sense, the line model is strongly related to circuit-switched networks, wormhole routing, optical networks supporting wavelength division multiplexing, ATM switching, and networks supporting connected mode routing protocols. Since the chordal rings are competitors of networks as meshes or tori because of theirs short diameter and bounded degree, it is of interest to ask whether they can support intensive communications (typically all-to-all) as efficiently as these networks. We propose polynomial algorithms to derive optimal or near optimal gossip protocols in the chordal ring

Approximable 1-Turn Routing Problems in All-Optical Mesh Networks

In all-optical networks, several communications can be transmitted through the same fiber link provided that they use different wavelengths. The MINIMUM ALL-OPTICAL ROUTING problem (given a list of pairs of nodes standing for as many point to point communication requests, assign to each request a route along with a wavelength so as to minimize the overall number of assigned wavelengths) has been paid a lot of attention and is known to be N P–hard. Rings, trees and meshes have thus been investigated as specific networks, but leading to just as many N P–hard problems. This paper investigates 1-turn routings in meshes (paths are allowed one turn only). We first show the MINIMUM LOAD 1-TURN ROUTING problem to be N P–hard but 2-APX (more generally, the MINIMUM LOAD k-CHOICES ROUTING problem is N P–hard but k-APX), then that the MINIMUM 1-TURN PATHS COLOURING problem is 4-APX (more generally, any d-segmentable routing of load L in a hypermesh of dimension d can be coloured with 2d(L−1)+1 colours at most). >From there, we prove the MINIMUM ALL-OPTICAL 1-TURN ROUTING problem to be APX

Self-stabilizing network orientation algorithms in arbitrary rooted networks

Network orientation is the problem of assigning different labels to the edges at each processor, in a globally consistent manner. A self-stabilizing protocol guarantees that the system will arrive at a legitimate state in finite time, irrespective of the initial state of the system. Two deterministic distributed network orientation protocols on arbitrary rooted, asynchronous networks are proposed in this work. Both protocols set up a chordal sense of direction in the network. The protocols are self-stabilizing, meaning that starting from an arbitrary state, the protocols are guaranteed to reach a state in which every processor has a valid node label and every link has a valid edge label. The first protocol assumes an underlying depth-first token circulation protocol; it orients the network as the token is passed among the nodes and stabilizes in O(n) steps after the token circulation stabilizes, where n is the number of processors in the network. The second protocol is designed on an underlying spanning tree protocol and stabilizes in O(h) time, after the spanning tree is constructed, where h is the height of the spanning tree. Although the second protocol assumes the existence of a spanning tree of the rooted network, it orients all edges--both tree and non-tree edges--of the network

Resource reservation protocols for optical burst switched networks

Nesta disserta c~ao e feito um estudo em redes com comuta c~ao optica de agregados de pacotes (redes OBS). Assim, este estudo apresenta e descreve os conceitos mais importantes relacionados com as redes OBS. Inicialmente e analisado o estado da arte, efectuando uma descri c~ao detalhada da arquitectura de uma rede OBS. Seguidamente analisam-se os protocolos de reserva unidireccional de recursos (JIT, JIT+, JET, Jumpstart, Horizon and E-JIT). Para isso s~ao utilizadas redes com topologias regulares (em anel e em malha) com um n umero vari avel de n os, e tamb em irregulares (NSFNET e ARPANET). E tamb em apresentado um novo protocolo de reserva unidireccional de recursos chamado E-JIT+. Este novo protocolo baseia-se no protocolo j a existente JIT+ e tenta optimizar o seu desempenho. Para melhor descrever o modo de opera c~ao deste protocolo proposto e apresentada a especi ca c~ao formal do mesmo. Depois da apresenta c~ao deste protocolo analisa-se o seu desempenho. Para isso s~ao utilizadas as topologias de rede referidas anteriormente e tamb em um simulador de redes OBS adaptado de forma a suportar o novo protocolo. O simulador utilizado, de nome OBSSimulator, devolve os valores de probabilidade de perda dos agregados de pacotes em cada salto (hop) na rede. Deste modo, foram considerados v arios factores que podem in uenciar o desempenho dos protocolos de reserva unidireccional de recursos, tais como o n umero de n os da topologia de rede utilizada, a quantidade de tr afego na rede, o ganho do grau nodal, o tempo de processamento das mensagens de setup e o tempo de con gura c~ao dos comutadores opticos. No m deste trabalho concluiu-se que o protocolo proposto, E-JIT+, melhora o desempenho em rela c~ao aos outros protocolos de reserva unidireccional de recursos estudados, nos casos estudados