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## Métodos heurísticos e exatos para o problemas de roteamento em arcos capacitado e aberto = : Heuristic and exact approaches for the open capacitated arc routing problem; Heuristic and exact approaches for the open capacitated arc routing problem

Fonte: Biblioteca Digital da Unicamp
Publicador: Biblioteca Digital da Unicamp

Tipo: Tese de Doutorado
Formato: application/pdf

Publicado em 13/02/2012
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#Roteamento (Administração de redes de computadores)#Heurística#Programação heuristica#GRASP (Sistema operacional de computador)#Routing administration (computer networks)#Method of scanning#Heuristics#Heuristic programming#GRASP (computer operating system)

O problema de roteamento em arcos capacitado e aberto (open capacitated arc routing problem, OCARP) é um problema de otimização combinatorial NP-difícil em que, dado um grafo não-direcionado, o objetivo consiste em encontrar um conjunto de rotas de custo mínimo para veículos com capacidade restrita que atendam a demanda de um subconjunto de arestas. O OCARP está relacionado com o problema de roteamento em arcos capacitado (capacitated arc routing problem, CARP), mas difere deste pois o OCARP não possui um nó depósito e as rotas não estão restritas a ciclos. Aplicações da literatura para o OCARP são discutidas. Uma formula ção de programação linear inteira é fornecida junto com propriedades do problema. Uma metaheurística GRASP (greedy randomized adaptive search procedure) com reconexão por caminhos (path-relinking) é proposta e comparada com outras metaheurísticas bem-sucedidas da literatura. Algumas características do GRASP são: (i) ajuste reativo de parâmetros, cujos valores são estocasticamente selecionados com viés `aqueles valores que produziram, em média, as melhores soluções; (ii) um filtro estatístico que descarta soluções iniciais caso estas tenham baixa probabilidade de superar a melhor solução incumbente; (iii) uma busca local infactível que gera soluções de baixo custo utilizadas para explorar fronteiras factíveis/infactíveis do espaço de soluções; (iv) a reconexão por caminhos evolutiva aprimora progressivamente um conjunto de soluções de elevada qualidade (soluções elites). Testes computacionais foram conduzidos com instâncias CARP e OCARP e os resultados mostram que o GRASP é bastante competitivo...

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## Scale-free networks and scalable interdomain routing

Fonte: Faculdade de Ciências e Tecnologia
Publicador: Faculdade de Ciências e Tecnologia

Tipo: Dissertação de Mestrado

Publicado em //2010
Português

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Trabalho apresentado no âmbito do Mestrado em Engenharia Informática, como requisito parcial para obtenção do grau de Mestre em Engenharia Informática; The exponential growth of the Internet, due to its tremendous success, has brought to light some limitations of the current design at the routing and arquitectural level, such as scalability and convergence as well as the lack of support for traffic engineering, mobility, route differentiation and security.
Some of these issues arise from the design of the current architecture, while others are
caused by the interdomain routing scheme - BGP. Since it would be quite difficult to add support for the aforementioned issues, both in the interdomain architecture and in the in the routing scheme, various researchers believe that a solution can only achieved via a new architecture and (possibly) a new routing scheme.
A new routing strategy has emerged from the studies regarding large-scale networks, which
is suitable for a special type of large-scale networks which characteristics are independent of network size: scale-free networks. Using the greedy routing strategy a node routes a message to a given destination using only the information regarding the destination and its neighbours...

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## A Distributed Geo-Routing Algorithm for Wireless Sensor Networks

Fonte: Molecular Diversity Preservation International (MDPI)
Publicador: Molecular Diversity Preservation International (MDPI)

Tipo: Artigo de Revista Científica

Publicado em 27/05/2009
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Geographic wireless sensor networks use position information for greedy routing. Greedy routing works well in dense networks, whereas in sparse networks it may fail and require a recovery algorithm. Recovery algorithms help the packet to get out of the communication void. However, these algorithms are generally costly for resource constrained position-based wireless sensor networks (WSNs). In this paper, we propose a void avoidance algorithm (VAA), a novel idea based on upgrading virtual distance. VAA allows wireless sensor nodes to remove all stuck nodes by transforming the routing graph and forwarding packets using only greedy routing. In VAA, the stuck node upgrades distance unless it finds a next hop node that is closer to the destination than it is. VAA guarantees packet delivery if there is a topologically valid path. Further, it is completely distributed, immediately responds to node failure or topology changes and does not require planarization of the network. NS-2 is used to evaluate the performance and correctness of VAA and we compare its performance to other protocols. Simulations show our proposed algorithm consumes less energy, has an efficient path and substantially less control overheads.

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## Relaxing Routing Table to Alleviate Dynamism in P2P Systems

Fonte: MIT - Massachusetts Institute of Technology
Publicador: MIT - Massachusetts Institute of Technology

Tipo: Artigo de Revista Científica
Formato: 85408 bytes; application/pdf

Português

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In dynamic P2P networks, nodes join and depart from the system frequently, which partially damages the predefined P2P structure, and impairs the system performance such as basic lookup functionality. Therefore stabilization process has to be done to restore the logical topology. This paper presents an approach to relax the requirement on routing tables to provide provably better stability than fixed structured P2P systems. We propose a relaxed Chord that keeps the O(logN) number of hops for greedy lookup, but it requires less stabilization overhead. It allows a tradeoff between lookup efficiency and structure flexibility without adding any overhead to the system. In the relaxed routing structure, each routing entry ("finger") of the node is allowed to vary within a set of values. Each node only needs to keep a certain number of fingers that point to nodes in its anchor set. This relaxation reduces the burden of state management of the node. The relaxed routing scheme provides an alternative structure other than randomized P2P and deterministic P2P, by relaxing on finger selection. It provides good flexibility and therefore extends the system functioning time.; Singapore-MIT Alliance (SMA)

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## Energy-efficient beaconless geographic routing in wireless sensor networks

Fonte: IEEE Computer Soc
Publicador: IEEE Computer Soc

Tipo: Artigo de Revista Científica

Publicado em //2010
Português

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Geographic routing is an attractive localized routing scheme for wireless sensor networks (WSNs) due to its desirable scalability and efficiency. Maintaining neighborhood information for packet forwarding can achieve a high efficiency in geographic routing, but may not be appropriate for WSNs in highly dynamic scenarios where network topology changes frequently due to nodes mobility and availability. We propose a novel online routing scheme, called Energy-efficient Beaconless Geographic Routing (EBGR), which can provide loop-free, fully stateless, energy-efficient sensor-to-sink routing at a low communication overhead without the help of prior neighborhood knowledge. In EBGR, each node first calculates its ideal next-hop relay position on the straight line toward the sink based on the energy-optimal forwarding distance, and each forwarder selects the neighbor closest to its ideal next-hop relay position as the next-hop relay using the Request-To-Send/Clear-To-Send (RTS/CTS) handshaking mechanism. We establish the lower and upper bounds on hop count and the upper bound on energy consumption under EBGR for sensor-to-sink routing, assuming no packet loss and no failures in greedy forwarding. Moreover, we demonstrate that the expected total energy consumption along a route toward the sink under EBGR approaches to the lower bound with the increase of node deployment density. We also extend EBGR to lossy sensor networks to provide energy-efficient routing in the presence of unreliable communication links. Simulation results show that our scheme significantly outperforms existing protocols in wireless sensor networks with highly dynamic network topologies.; Haibo Zhang and Hong Shen

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## Metaheurísticas híbridas aplicadas al problema de ruteo de arcos capacitados; Hybrid metaheuristics for the capacitated arc routing problem

Fonte: Facultad de Ciencias Exactas y Naturales. Universidad de Buenos Aires
Publicador: Facultad de Ciencias Exactas y Naturales. Universidad de Buenos Aires

Tipo: info:eu-repo/semantics/doctoralThesis; tesis doctoral; info:eu-repo/semantics/publishedVersion
Formato: application/pdf

Publicado em //2011
Português

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#BRKGA#CAPACITATED ARC ROUTING PROBLEM#GRASP#HBMO#METAHEURISTICS#SCATTER SEARCH#TABU SEARCH#VEHICLE ROUTING#VNS#BRKGA#GRASP

El Problema de Ruteo de Arcos Capacitados (CARP) es un problema de optimización combinatoria que consiste en satisfacer demandas de servicios/productos sobre determi- nadas calles de una red vial mediante una flota homogénea de vehículos, minimizando el costo total de recorrido involucrado. Ha sido aplicado a casos reales como recolección de residuos, mantenimiento de calles, lectura de medidores eléctricos, entre otros. CARP es un problema de optimización combinatoria de tipo NP-Hard. A tal efecto, en la literatura se han propuesto algoritmos exactos y heurísticas. Los primeros, basados en su mayoría en las técnicas Branch and Bound y Cutting Plane, obtienen soluciones óptimas sobre instancias de datos de tamaño reducido. Los segundos, en general, alcanzan soluciones cercanas a las óptimas y a bajo costo computacional. El objetivo de esta tesis es el desarrollo de algoritmos heurísticos que contengan ca- racterísticas salientes de metaheurísticas tales como Honey Bee Mating Optimization (HBMO), Biased Random Key Genetic Algorithm (BRKGA), Greedy Randomized Adaptive Search Procedure (GRASP), Variable Neighborhood Search (VNS), entre otras. Los resultados computacionales obtenidos por los algoritmos propuestos usando diferentes instancias de la literatura...

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## Papillon: Greedy Routing in Rings

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/07/2005
Português

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#Computer Science - Distributed, Parallel, and Cluster Computing#Computer Science - Networking and Internet Architecture

We study {\sc greedy} routing over $n$ nodes placed in a ring, with the
\emph{distance} between two nodes defined to be the clockwise or the absolute
distance between them along the ring. Such graphs arise in the context of
modeling social networks and in routing networks for peer-to-peer systems. We
construct the first network over $n$ nodes in which {\sc greedy} routing takes
$O(\log n / \log d)$ hops in the worst-case, with $d$ out-going links per node.
Our result has the first asymptotically optimal greedy routing complexity.
Previous constructions required $O(\frac{\log^2 n}{d})$ hops.

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## Efficient Greedy Geographical Non-Planar Routing with Reactive Deflection

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 24/02/2009
Português

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We present a novel geographical routing scheme for spontaneous wireless mesh
networks. Greedy geographical routing has many advantages, but suffers from
packet losses occurring at the border of voids. In this paper, we propose a
flexible greedy routing scheme that can be adapted to any variant of
geographical routing and works for any connectivity graph, not necessarily Unit
Disk Graphs. The idea is to reactively detect voids, backtrack packets, and
propagate information on blocked sectors to reduce packet loss. We also propose
an extrapolating algorithm to reduce the latency of void discovery and to limit
route stretch. Performance evaluation via simulation shows that our modified
greedy routing avoids most of packet losses.

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## Succint greedy routing without metric on planar triangulations

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 28/04/2015
Português

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#Computer Science - Networking and Internet Architecture#Computer Science - Computational Geometry#05C10#C.2.1

Geographic routing is an appealing routing strategy that uses the location
information of the nodes to route the data. This technique uses only local
information of the communication graph topology and does not require
computational effort to build routing table or equivalent data structures. A
particularly effi?cient implementation of this paradigm is greedy routing,
where along the data path the nodes forward the data to a neighboring node that
is closer to the destination. The decreasing distance to the destination
implies the success of the routing scheme. A related problem is to consider an
abstract graph and decide whether there exists an embedding of the graph in a
metric space, called a greedy embedding, such that greedy routing guarantees
the delivery of the data. In the present paper, we use a metric-free de?nition
of greedy path and we show that greedy routing is successful on planar
triangulations without considering the existence of greedy embedding. Our
algorithm rely entirely on the combinatorial description of the graph structure
and the coordinate system requires O(log(n)) bits where n is the number of
nodes in the graph. Previous works on greedy routing make use of the embedding
to route the data. In particular, in our framework...

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## On the Necessary and Sufficient Condition of Greedy Routing Supporting Geographical Data Networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/03/2009
Português

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Large scale decentralized communication systems have introduced the new trend
towards online routing where routing decisions are performed based on a limited
and localized knowledge of the network. Geometrical greedy routing has been
among the simplest and most common online routing schemes. A perfect
geometrical routing scheme is expected to deliver each packet to the point in
the network that is closest to the packet destination. However greedy routing
fails to guarantee such delivery as the greedy forwarding decision sometimes
leads the packets to localized minimums. This article investigates the
necessary and sufficient properties of the greedy supporting graphs that
provide the guaranteed delivery of packets when acting as a routing substrate.

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## Tight Lower Bounds for Greedy Routing in Higher-Dimensional Small-World Grids

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 06/05/2013
Português

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#Computer Science - Data Structures and Algorithms#Computer Science - Computational Complexity#Computer Science - Networking and Internet Architecture#Computer Science - Social and Information Networks

We consider Kleinberg's celebrated small world graph model (Kleinberg, 2000),
in which a D-dimensional grid {0,...,n-1}^D is augmented with a constant number
of additional unidirectional edges leaving each node. These long range edges
are determined at random according to a probability distribution (the
augmenting distribution), which is the same for each node. Kleinberg suggested
using the inverse D-th power distribution, in which node v is the long range
contact of node u with a probability proportional to ||u-v||^(-D). He showed
that such an augmenting distribution allows to route a message efficiently in
the resulting random graph: The greedy algorithm, where in each intermediate
node the message travels over a link that brings the message closest to the
target w.r.t. the Manhattan distance, finds a path of expected length O(log^2
n) between any two nodes. In this paper we prove that greedy routing does not
perform asymptotically better for any uniform and isotropic augmenting
distribution, i.e., the probability that node u has a particular long range
contact v is independent of the labels of u and v and only a function of
||u-v||.
In order to obtain the result, we introduce a novel proof technique: We
define a budget game, in which a token travels over a game board...

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## Category-Based Routing in Social Networks: Membership Dimension and the Small-World Phenomenon (Full)

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/10/2011
Português

Relevância na Pesquisa

38.435215%

#Computer Science - Social and Information Networks#Computer Science - Data Structures and Algorithms#Physics - Physics and Society

A classic experiment by Milgram shows that individuals can route messages
along short paths in social networks, given only simple categorical information
about recipients (such as "he is a prominent lawyer in Boston" or "she is a
Freshman sociology major at Harvard"). That is, these networks have very short
paths between pairs of nodes (the so-called small-world phenomenon); moreover,
participants are able to route messages along these paths even though each
person is only aware of a small part of the network topology. Some sociologists
conjecture that participants in such scenarios use a greedy routing strategy in
which they forward messages to acquaintances that have more categories in
common with the recipient than they do, and similar strategies have recently
been proposed for routing messages in dynamic ad-hoc networks of mobile
devices. In this paper, we introduce a network property called membership
dimension, which characterizes the cognitive load required to maintain
relationships between participants and categories in a social network. We show
that any connected network has a system of categories that will support greedy
routing, but that these categories can be made to have small membership
dimension if and only if the underlying network exhibits the small-world
phenomenon.; Comment: 12 pages

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## Greedy routing on networks of mobile agents

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/12/2011
Português

Relevância na Pesquisa

48.81092%

#Computer Science - Networking and Internet Architecture#Physics - Data Analysis, Statistics and Probability

In this paper, we design a greedy routing on networks of mobile agents. In
the greedy routing algorithm, every time step a packet in agent $i$ is
delivered to the agent $j$ whose distance from the destination is shortest
among searched neighbors of agent $i$. Based on the greedy routing, we study
the traffic dynamics and traffic-driven epidemic spreading on networks of
mobile agents. We find that the transportation capacity of networks and the
epidemic threshold increase as the communication radius increases. For moderate
moving speed, the transportation capacity of networks is the highest and the
epidemic threshold maintains a large value. These results can help controlling
the traffic congestion and epidemic spreading on mobile networks.

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## Near Optimal Routing for Small-World Networks with Augmented Local Awareness

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Computer Science - Discrete Mathematics#Computer Science - Distributed, Parallel, and Cluster Computing#Computer Science - Data Structures and Algorithms

In order to investigate the routing aspects of small-world networks,
Kleinberg proposes a network model based on a $d$-dimensional lattice with
long-range links chosen at random according to the $d$-harmonic distribution.
Kleinberg shows that the greedy routing algorithm by using only local
information performs in $O(\log^2 n)$ expected number of hops, where $n$
denotes the number of nodes in the network. Martel and Nguyen have found that
the expected diameter of Kleinberg's small-world networks is $\Theta(\log n)$.
Thus a question arises naturally: Can we improve the routing algorithms to
match the diameter of the networks while keeping the amount of information
stored on each node as small as possible? We extend Kleinberg's model and add
three augmented local links for each node: two of which are connected to nodes
chosen randomly and uniformly within $\log^2 n$ Mahattan distance, and the
third one is connected to a node chosen randomly and uniformly within $\log n$
Mahattan distance. We show that if each node is aware of $O(\log n)$ number of
neighbors via the augmented local links, there exist both non-oblivious and
oblivious algorithms that can route messages between any pair of nodes in
$O(\log n \log \log n)$ expected number of hops...

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## Aligned Virtual Coordinates for Greedy Routing in WSNs

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/05/2006
Português

Relevância na Pesquisa

49.00927%

Geographic routing provides relatively good performance at a much lower
overhead than conventional routing protocols such as AODV. However, the
performance of these protocols is impacted by physical voids, and localization
errors. Accordingly, virtual coordinate systems (VCS) were proposed as an
alternative approach that is resilient to localization errors and that
naturally routes around physical voids. However, we show that VCS is vulnerable
to different forms of the void problem and the performance of greedy routing on
VCS is worse than that of geographic forwarding. We show that these anomalies
are due to the integral nature of VCS, which causes quantization noise in the
estimate of connectivity and node location. We propose an aligned virtual
coordinate system (AVCS) on which the greedy routing success can be
significantly improved. With our approach, and for the first time, we show that
greedy routing on VCS out-performs that on physical coordinate systems even in
the absence of localization errors. We compare AVCS against some of the most
popular geographical routing protocols both on physical coordinate system and
the virtual coordinate systems and show that AVCS significantly improves
performance over the best known solutions.

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## Scalable Routing Easy as PIE: a Practical Isometric Embedding Protocol (Technical Report)

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/05/2013
Português

Relevância na Pesquisa

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We present PIE, a scalable routing scheme that achieves 100% packet delivery
and low path stretch. It is easy to implement in a distributed fashion and
works well when costs are associated to links. Scalability is achieved by using
virtual coordinates in a space of concise dimensionality, which enables greedy
routing based only on local knowledge. PIE is a general routing scheme, meaning
that it works on any graph. We focus however on the Internet, where routing
scalability is an urgent concern. We show analytically and by using simulation
that the scheme scales extremely well on Internet-like graphs. In addition, its
geometric nature allows it to react efficiently to topological changes or
failures by finding new paths in the network at no cost, yielding better
delivery ratios than standard algorithms. The proposed routing scheme needs an
amount of memory polylogarithmic in the size of the network and requires only
local communication between the nodes. Although each node constructs its
coordinates and routes packets locally, the path stretch remains extremely low,
even lower than for centralized or less scalable state-of-the-art algorithms:
PIE always finds short paths and often enough finds the shortest paths.; Comment: This work has been previously published in IEEE ICNP'11. The present
document contains an additional optional mechanism...

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## Category-Based Routing in Social Networks: Membership Dimension and the Small-World Phenomenon (Short)

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/08/2011
Português

Relevância na Pesquisa

38.435215%

#Computer Science - Social and Information Networks#Computer Science - Data Structures and Algorithms#Physics - Physics and Society

A classic experiment by Milgram shows that individuals can route messages
along short paths in social networks, given only simple categorical information
about recipients (such as "he is a prominent lawyer in Boston" or "she is a
Freshman sociology major at Harvard"). That is, these networks have very short
paths between pairs of nodes (the so-called small-world phenomenon); moreover,
participants are able to route messages along these paths even though each
person is only aware of a small part of the network topology. Some sociologists
conjecture that participants in such scenarios use a greedy routing strategy in
which they forward messages to acquaintances that have more categories in
common with the recipient than they do, and similar strategies have recently
been proposed for routing messages in dynamic ad-hoc networks of mobile
devices. In this paper, we introduce a network property called membership
dimension, which characterizes the cognitive load required to maintain
relationships between participants and categories in a social network. We show
that any connected network has a system of categories that will support greedy
routing, but that these categories can be made to have small membership
dimension if and only if the underlying network exhibits the small-world
phenomenon.

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## Hierarchical Bipartition Routing for delivery guarantee in sparse wireless ad hoc sensor networks with obstacles

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 08/07/2013
Português

Relevância na Pesquisa

38.633562%

We introduce and evaluate a very simple landmark-based network partition
technique called Hierarchical Bipartition Routing (HBR) to support routing with
delivery guarantee in wireless ad hoc sensor networks. It is a simple routing
protocol that can easily be combined with any other greedy routing algorithm to
obtain delivery guarantee. The efficiency of HBR increases if the network is
sparse and contains obstacles. The space necessary to store the additional
routing information at a node u is on average not larger than the size
necessary to store the IDs of the neighbors of u. The amount of work to setup
the complete data structure is on average proportional to flooding the entire
network log(n) times, where n is the total number of sensor nodes. We evaluate
the performance of HBR in combination with two simple energy-aware geographic
greedy routing algorithms based on physical coordinates and virtual
coordinates, respectively. Our simulations show that the difference between
using HBR and a weighted shortest path to escape a dead-end is only a few
percent in typical cases.; Comment: Presented on the ICWN 2012, Las Vegas

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## A stochastic analysis of greedy routing in a spatially dependent sensor network

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

48.09637%

For a sensor network, a tractable spatially-dependent node deployment model
is presented with the property that the density is inversely proportional to
the sink distance. A stochastic model is formulated to examine message
advancements under greedy routing in such a sensor network. The aim of this
work is to demonstrate that an inhomogeneous Poisson process can be used to
model a sensor network with spatially-dependent node density. Elliptic
integrals and asymptotic approximations are used to describe the random
behaviour of hops. Types of dependence that affect hop advancements are
examined. We observe that the dependence between successive jumps in a multihop
path is captured by including only the previous forwarding node location. We
include a simple uncoordinated sleep scheme, and observe that the complexity of
the model is reduced when enough nodes are asleep. All expressions involving
multidimensional integrals are derived and evaluated with quasi-Monte Carlo
integration methods based on Halton sequences and recently-developed lattice
rules. An importance sampling function is derived to speed up the quasi-Monte
Carlo methods. The ensuing results agree extremely well with simulations.

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## Improving Routing Efficiency through Intermediate Target Based Geographic Routing

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 15/02/2015
Português

Relevância na Pesquisa

38.746284%

The greedy strategy of geographical routing may cause the local minimum
problem when there is a hole in the routing area. It depends on other
strategies such as perimeter routing to find a detour path, which can be long
and result in inefficiency of the routing protocol. In this paper, we propose a
new approach called Intermediate Target based Geographic Routing (ITGR) to
solve the long detour path problem. The basic idea is to use previous
experience to determine the destination areas that are shaded by the holes. The
novelty of the approach is that a single forwarding path can be used to
determine a shaded area that may cover many destination nodes. We design an
efficient method for the source to find out whether a destination node belongs
to a shaded area. The source then selects an intermediate node as the tentative
target and greedily forwards packets to it, which in turn forwards the packet
to the final destination by greedy routing. ITGR can combine multiple shaded
areas to improve the efficiency of representation and routing. We perform
simulations and demonstrate that ITGR significantly reduces the routing path
length, compared with existing geographic routing protocols.

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