OPTICAL MULTICAST ROUTING

1
OPTICAL MULTICASTROUTING
2
Outlines

• Introduction
• Multicast Routing Problem
• Node Architecture
• OMMP
• Multicast Routing Problem

3
Introduction

• Traditional communication models have been
• one-to-one or unicast, and
• one-to-all or broadcast.
• Between these two extremes lies multicast,
• the targeting of a data stream to a selected set
  of receivers.
• This model is used to characterize the
  communication patterns in a wide spectrum of
  applications such as
• replicated databases,
• command and control systems,
• distributed games,
• audio/video conferencing, and
• distributed interactive simulation.

4
Introduction

• The following are some applications that make use
  of multicast communication.
• Multimedia A number of users "tune in" to a
  video or audio transmission from a multimedia
  source station.
• Teleconferencing A group of workstations forms a
  multicast group so that a transmission from any
  member is received by all other group members.
• Databases All copies of a replicated file or
  database are updated at the same time.
• Distributed computation Intermediate results are
  sent to all participants in a distributed
  computation.
• Real-time workgroups Files, graphics, and
  messages are exchanged among active group members
  in real time.

5
Introduction

• A good communication network which provides a
  multicast transmission system should have
  properties such as
• high probability of delivery of information,
• low delay between source and destinations, and
• Information hiding from intermediate routers.
• These properties can be achieved by using optical
  signals instead of electrical signals to transfer
  the information.
• The optical medium will also provide enormous
  bandwidth (tens of terahertz). It is very
  difficult to exploit such a high bandwidth as a
  single channel. Hence the complete bandwidth is
  channelized, with different wavelengths using
  WDM.

6
Introduction

• Among the WDM optical networks, wavelength routed
  networks are becoming popular for wide area
  networks.
• To support multicasting, in wavelength routed
  networks, the routing nodes should have the
  capability of optical splitting.
• If it is assumed that every node in the network
  has optical splitting capability and wavelength
  conversion capability, then the problem of
  multicast routing boils down to the problem of
  multicast routing in electronic networks.
• However, split-capable nodes are costlier than
  wavelength routing nodes without split
  capability.
• Hence it is suggested that only a few nodes in
  the network be allowed to have splitting
  capability.
• The multicast routing problem in wavelength
  routed networks is addressed in this chapter.

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Multicast Routing Problem

• A WDM network employing wavelength routing
  consists of optical wavelength routing nodes
  interconnected by point to point fiber links in
  an arbitrary topology.
• The optical routing nodes do have the capability
  of switching a wavelength individually.
• A wavelength routing node may have the capability
  to tap a small amount of optical power from the
  wavelength channel which is forwarded by that
  node.
• The tapped optical power may be used by the local
  node. This type of node is called as a drop and
  continue node (DaC node) (Tap and Continuous)
  5, 197.

8
Conventional v.s. WDM

• To support multicasting, in a conventional
  network (electronic network), all nodes are
  assumed to have the capability of buffering an
  incoming message and transmitting it onto more
  than one output link.
• To support multicasting in a WDM network, nodes
  in the network need to have light (optical)
  splitting capability.
• A node with splitting capability can forward an
  incoming message to more than one output link.
• If a network has splitting capability at all
  nodes, then it is referred to as a network with
  full splitting capability.
• In a network with full splitting capability, a
  single tree can be generated to include all the
  destinations of a multicast session, as in a
  conventional electronic network 124, 151.

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sparse splitting capability

• A tree refers to a set of destinations connected
  together with a source as the root.
• The source needs to transmit a message only once
  to communicate to all the destinations belonging
  to the same tree.
• A split-capable node is very expensive due to its
  complex architecture 197. Hence only a subset
  of the nodes in a network are assumed to be
  split-capable nodes.
• A network with a few split-capable nodes is
  called a network with sparse splitting capability
  92.
• In a network with sparse splitting capability, it
  may not be possible to include all destinations
  of a session in one multicast tree.
• Hence a set of trees is constructed to include
  all destinations of a multicast session.
• This means that the source needs to transmit the
  multicast data onto more than one channel, maybe
  on different fibers or on different wavelengths.
• The set of trees corresponding to a single
  multicast session is called a multicast forest
  92, 159, 197.

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Multicast Routing Problem

• A network with sparse wavelength conversion and
  sparse splitting capability consists of nodes
  with different capabilities.
• A node may have splitting capability and/or
  wavelength conversion capability.
• In general, a node with split capability is
  called a multicast-capable node (MC node).
• A node with only splitting capability is called a
  split node, and
• A DaC node with wavelength conversion capability
  is termed a wavelength conversion node (WC node).
  
• A node having both splitting and wavelength
  conversion capabilities is called a virtual
  source (VS). A VS node can transmit an incoming
  message to any number of output links on any
  wavelength.

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Multicast Routing Problem

• A split node and a VS node are used for expanding
  the tree.
• A part of the tree which is expanded from a split
  node or VS node is called a subtree.
• The difference between a split node and a VS node
  is that a split node cannot support more than one
  connection on the same outgoing link, whereas a
  VS does support by using different wavelengths.
• This means that the subtree spawned from a VS may
  use the same physical link which is used by the
  existing connection but on a different
  wavelength.
• A node without splitting capability is called a
  multicast-incapable node (MI node).
• An MI node may have the capability of drop and
  continue or it may have no such capability.
• A node without any capability is an ordinary
  wavelength router, and it can either drop a
  message or can switch a message, but not both
  operations simultaneously.
• Hence, for consistency, such a node can be
  called a drop or continue node (DoC node).

13
Node Architecture of MC nodes
14
Node Architecture of MC nodes

• An MC node consists of optical power splitters.
• To support multicast, the input signal needs to
  be transmitted onto various output connections.
  These connections may be on different links
  connected to the node or on different wavelength
  channels of the same fiber.
• If a node has n input links with a single fiber
  per link, and each fiber consists of W number of
  wavelengths, then to support multicast the input
  signal needs to be selected by n x W number of
  switches.

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MC nodes

• However, this wavelength conversion stage is an
  optional one. An MC node need not perform
  wavelength conversion.
• Finally, for each output link, one multiplexer is
  present so that the signals on various
  wavelengths are multiplexed and transmitted onto
  the same fiber.
• In general, for an MC node with n input links, m
  output links, and W wavelengths per fiber, there
  are n number of 1 x m splitters, n x m number of
  1 x W optical splitters, m x W number of n x 1 SD
  switches, m x W number of TFs and wavelength
  converters, and m multiplexers.
• Power amplification is required to compensate for
  the power loss due to splitting operation.

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Architecture of an MI Node

• A node without splitting capability is called a
  multicast-incapable node or an MI node.
• MI nodes may tap (or drop) a small fraction of
  signal and switch the remaining signal to one of
  its neighbor nodes. The tapped (dropped) signal
  may be used by the local station.
• This type of node which can tap or drop the
  signal passing through it is called as a DaC
  node.
• The architecture of a DaC node is shown in Fig.
  8.3. Here, the input signal is demultiplexed and
  each of these demultiplexed signals is fed as
  input to the "tap" (drop) module which taps 5 of
  signal.
• Then, as in a conventional wavelength routed
  node, the signal is switched using SD switches.

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MULTICAST TREE GENERATION

• Multicasting is the process of transmitting data
  by a source to a set of destinations.
• Instead of transmitting packets from a sender to
  each receiver, the routes between source and
  receivers can share some links.
• In conventional networks, multicast route
  determination is traditionally formulated as a
  problem related to tree construction 161.

19
Tree construction

• The reasons for adapting tree structure for
  multicast communication are listed below.
• The source need not send a packet to individual
  destinations.
• The packets are transmitted in parallel to
  various destinations.
• The tree structure minimizes data replication,
  since the packet is replicated optically by
  routers only at branch points in the tree.

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Overview

• In a network with full splitting capability, a
  single tree can be generated to include all the
  destinations of a multicast session, as in a
  conventional electronic network 124, 151,
  152.
• Hence, in a network with full splitting
  capability, the constraints to generate a
  multicast tree would be minimizing the number of
  transceivers and wavelengths in a fiber.
• In a network with sparse splitting capability, it
  may not be possible to include all the
  destinations of a session in one multicast tree.
• Hence, a set of trees is constructed to include
  all the destinations of a multicast session. This
  means that the source needs to transmit the
  multicast data onto more than one channel and
  maybe on different fibers or on different
  wavelengths. The set of trees corresponding to a
  single session is called a multicast forest.

21
DaC network

• In a densely connected network, the number of
  splitters required in a node is high. Hence it is
  difficult and also expensive to fabricate such a
  node.
• Also, the optical power splitting causes loss in
  the optical signal and hence optical amplifiers
  are required.
• In 5, a new tree generation algorithm is
  proposed which uses only DaC capability of a
  node.
• First, a directed graph is constructed for the
  given network. Then, an optimal trail, which
  starts from the source of a multicast session and
  visits all destinations, is computed.

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multiple-destination minimum-cost trail MDMCT)

• A trail is a path where nodes are allowed to be
  visited more than once.
• A node, if it is a destination, taps a small
  amount of optical signal. In 5,
• it is stated that constructing a trail with an
  objective of minimizing the number of directed
  edges (also referred to as multiple-destination
  minimum-cost trail MDMCT) is an NP-complete
  problem.
• Hence a heuristic is presented in which first a
  Steiner tree is constructed using a minimum path
  heuristic 168, then a trail is computed around
  the Steiner tree.
• Even though this method of constructing a
  multicast tree avoids using optical split at the
  nodes, it requires more number of wavelength
  channels.
• This is because every link in the Steiner tree is
  traversed twice, once in each direction.

23
Multicast Tree Generation

• Full Splitting Capability all nodes in the
  network have split capability.
• Hence, a single tree can be generated to route
  multicast traffic.
• The tree generation is similar to the tree
  generation in conventional networks. Apart from
  finding a path, in a conventional network it is
  necessary to allocate bandwidth and buffers.
• But in optical networks, the constraints are
  number of transceivers and wavelengths. Hence,
  the tree generation algorithm should consider the
  availability of these resources while generating
  a multicast tree.

24
Light-tree

• In 151, the problem of minimizing the number of
  transmitters and receivers that are required to
  generate a multicast tree is considered. It
  introduces the concept of a light-tree.
• A light-tree is a point-to-multipoint optical
  path established in the network created by
  allocating the same wavelength on every link of
  the tree.
• The concept of light-trees can be implemented by
  incorporating optical multicasting (splitting)
  capability at all nodes of a network in order to
  reduce the average packet hop distance and the
  total number of transceivers in a network.
• Thus, a light-tree provides single-hop
  communication between a source node and a set of
  destination nodes.
• A solution is provided in 151 for routing
  unicast traffic and broadcast traffic using
  light-trees.
• To carry unicast traffic, the virtual topology
  design problem is formulated based on the
  light-tree concept.

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• The proposed optimization problem has one of the
  following objective functions
• Minimize the network-wide average packet hop
  distance.
• Minimize the total number of transceivers in the
  network.
• In 151 it is demonstrated that the average
  packet hop distance for a virtual topology based
  on light-trees is less than that of a virtual
  topology based on the lightpath concept.
• It is also demonstrated that the number of
  transmitters and receivers required for the
  virtual topology based on light-trees is less
  than the number of transmitters and receivers
  required for the virtual topology designed based
  on the lightpath concept.
• For broadcast traffic, minimization of the number
  of transceivers is considered the objective
  function.
• The light-tree concept can also be applied to
  multicast traffic.

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Genetic Algorithms for Multiple Multicast Problem
on WDM Ring
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Problem Definition

• Ring network G(V,E)
• V the set of nodes
• E the set of links
• bi-directional link
• W wavelengths per link?

30
Problem Definition

• r groups of multicasts,
• Misi, Di,i1, 2, , r, 1?ki?nwhere
• Did1i, d2i, , dkii be the destination
• si source
• For each multicast Misi, Di,a multicast tree
  MTi is need
• Construct a multicast forest MFUi1,2,r MTi?
• Construct MF with wavelength continuity
  constraint, such the number of used wavelengths
  is minimized?

31
OMMP

• Optimal multiple multicast problem, OMMP
• ????WDM???r?????????????MMisi, Di,i1, 2, ,
  r, 1?ki?n,??????????,??????????????????,?????????
  ?????
• OMMP is a NP-hard problem
• Since RWA(NP-hard) is a special case of OMMP
• RWA on Ring is a NP-hard problem.

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Example
33
Possible Assignment of Example
34
Observation

• Each MTi can be constructed by
• ????????????Pc(si, dl-1i)
• ????????????Pr(si, dl1i)
• ??????,????????????Pr(si, dli) ?Pc(si,
  dli),????l?D?

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Model
36
Genetic Algorithm

• BeginInitialize populationwhile (not terminal
  condition) do Begin choose parents from
  population / Selection / construct offspring
  by combining parents / Crossover / optimize
  (offspring) / Mutation / if suited
  (offspring) then replace worst fit (population)
  with better offspring / Survival of the
  fittest / End
• End.

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Genetic Algorithm

• Chromosome Encoding
• Objective Function
• Penalty Function
• Crossover
• Mutation
• Selection

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Chromosome Encoding

• routing gene
• MGimgik, i1,...,r k1,2 AGiagik,
  i1,...,r k1,2
• r number of connections. r4

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Example of chromosome encoding
1
8
2
3
7
4
6
5
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Wavelength gene
41
Objective Function

• Objective function
• The assignment represented by the connection may
  not constraint-satisfy, thus, a penalty function
  should be included in objective function.

42
Penalty Function

• Assume both connections c1(1,2) and c2(1,4) are
  assigned to wavelength 1 with clockwise
  direction, then conflict occurred.
• Penalty should be defined.
• How to detect the conflict in a connection gene?
• A conflict-detection algorithm should be
  developed.
• O(M2) pairs of connections should be examined.
• The conflict between two connections can be
  detected in constant time O(1).

43
Graph AA
c4
c3
c1
c2

• c1(1,4) , c2(2,4) , c3(1,2) , c4(5,2)

44
Crossover Operators

• Single point crossover (SPC)
• Single point wavelength crossover (SPWC)
• Single point routing path crossover (SPWC)
• Single assigning wavelength exchanging operator
  (SAWEO)
• Wavelength exchanging operator (WEO)

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Mutations

• Single Routing Path Mutations (SRPM)
• Multiple Routing Paths Mutations (MRPM)
• Single wavelength assignment mutation (SWAM)
• Multiple wavelength assignment mutation (MWAM)
• Multicast assignment mutation (MAM)

46
Heuristic Algorithms

• 2-phase algorithm
• Routing phase
• Maximal-Gap Routing
• Minimal Load Routing
• Assignment Phase
• Greedy Wavelength Assign

47
Extended Genetic Algorithm

• Produce only feasible solutions
• No need for the penalty function
• The wavelength assigned to the multicast is
  determined by the greedy wavelength assign
  algorithm.

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Chromosome Encoding

• routing gene
• MGimgik, i1,...,r k1,2

49
Objective Function

• Objective function

50
Operators

• Crossover
• single point crossover
• Mutation
• Single routing path mutation (SRPM)
• Multiple routing paths mutation (MRPM)

51
Hybrid Genetic Algorithm

• To speed up algorithm
• Heuristic routing algorithms are used.
• HGA1 heuristics SGA
• HGA2 heuristics EGA

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Experiments

• Run on PC with a Pentium III 1GHz CPU and 512MB
  RAM.
• For nodes n100, 200, 300
• Two sets of multicast requests are randomly
  generated.
• Specific
• Random
• MAXM5, 10 the maximal number destinations in
  D.

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Specific Set
54
Specific Set

• Ranges Ai j n(i-1)/51 ? j ? ni/5
• The source and destination nodes of multicast Mi,
  i1,2,...,r are randomly selected from nodes in
  Ai and two of which are n(i-1)/51 and ni/5.
• The lower bound of the minimal used wavelengths
  of the set Mspecific is r/5.

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Specific n100 (MAXM 5 or 10)
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Specific n200 (MAXM 5 or 10)
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Specific n300 (MAXM 5 or 10)
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Random n100 (MAXM 5 or 10)
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Random n200 (MAXM 5 or 10)
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Random n300 (MAXM 5 or 10)
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More Improvement
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More Improvement
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Conclusion and Further Research

• Proposed
• Mathematic Model for multiple multicast problem
  on WDM ring
• Several Heuristic Algorithms
• Genetic Algorithms
• Further Research in the problem
• Lower bound proof
• CPLEX package to found optimal solution
• Other Soft-computing method
• Simulated Annealing, Tabu search, Ant algorithm,
  Scatter search

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Multicast Problem on WDM

• Multicast is a point to multipoint communication,
  by which a source node sends messages to multiple
  destination nodes.
• A light-tree, as a point to multipoint extension
  of a light-path, is a tree in the physical
  topology and occupies the same wavelength in all
  fiber links in the tree.
• Given an multicast request in a WDM network
  system, compute a set of routing trees and assign
  wavelengths to them such the cost is minimized.

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Assumptions

• Source node be the uniquely one has
  light-splitting function (multicast capable).
• Each node of the tree is a multicast-Incapable
  optical switch (MI node) (no light-splitting
  function) .
• Each node can perform drop and continue function.
• Single-hop WDM network
• All Optical Network
• Static Traffic

69
Introduction

• The problem is formalized as follows
• Given a multicast request in a WDM network
  system, compute a set of routing paths
  (light-trees) and assign wavelengths to them such
  that the total cost in minimized.
• The objective function has two components
• the number of used wavelengths
• the cost of light-tree
• The objective is minimize cost of light-tree plus
  the cost a(number of used wavelengths).

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System Models

• WDM network
• Connected and undirected graph
• G(V, E, c, w)
• V vertex-set
• E edge-set
• Each edge e in E is associated with two weight
  functions
• c(e) communication cost
• W the number of wavelengths provided by WDM
  network.

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System Models

• Cost of path P(u,v)
• A multicast request in the system are given,
  denoted by r (s, D)
• source s
• destination D

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System Models

• Tk (s, Dk) be the routing tree for request r (s,
  D) in wavelength k, where kltW.
• T? k1,2,...,WTk (s, Dk) D? k1,2,...,W Dk
• T is the light-forest, DinDj ?,for i?j.
• The light signal is forwarded to (continuous) the
  output port leading to its child, which then
  transmit the signal to its child until all nodes
  in the Dk receive it.

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Objective

• The cost of the light-tree Tk (s, Dk)
• The cost of the light-forest T is defined

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Total cost

• where yj 1 if wavelength j is used yj0,
  otherwise
• Special case
• One objective of the multicast routing is to
  construct a routing tree (or forest) which has
  the minimal cost. The problem is regarded as the
  minimum Steiner tree problem, which was proved to
  be NP-hard.
• Another objective is to minimize the number of
  wavelengths used in the system.

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Example
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Genetic Algorithm

• Basic idea modified the GA of R-H Whang et al.
  to WDM network

pi is between 1 and Ri, i1,2,...,D, where Ri
is the number of candidate path from s to di
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Chromosome Encoding
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Light-Forest Construct Algorithm(LFCA)

• Path by path construct
• Integrated the path and wavelength in single
  phase
• Step 1 Sort paths in increasing order according
  to the cost of each path O(D log D) time.
  Assume that p1,p2,...., pD be the new index.
• Step 2 p1 is assigned to wavelength 1,w1,
  T1p1, T2 ...Tkø. O(n)

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Light-Forest Construct Algorithm

• Step 3 For i 2 to D do
• Begin
• j1
• while j?w do
• if pi is not conflict with Tj
• then
• assigned pi to Tj
• TjTj ?pi
• flagTRUE
• else jj1
• if flag is not TRUE
• then
• ww1
• TwTw ? pi
• End

Time complexity O(D2n)
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Example
p1s?7 ?1 (10) p2s?7 ?14 ?2 (13) p3s?9 ?13 ?3
(15) p4s?10 ?4 (8) p5s?10 ?4 ?5 (12) p6s?9
?13 ?5 ?6 (26)
cost81041513262a
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Conflict Test

• light-tree is represented by a directed tree root
  at s.
• O(n) time add path into a directed tree, then
  test the out-degree of the visited vertex, if the
  out-degree gt1 then conflict occurred.

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Fitness Function

• The light-forest construct a feasible solution of
  the WDM network, thus, there is no need for the
  penalty function
• Minimized
• Transform to maximization form
• where Cmax denotes the maximum value observer so
  far of the cost function in the population.

Fitness Cmax - Cost
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Crossover Operator

• single point crossover
• multiple point crossover

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Single point Crossover
After crossover, the light-forest should be
reconstructed
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Multiple point Crossover

• After crossover, the light-forest should be
  reconstructed

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Mutation Operator

• single point mutation
• heuristic mutation

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Single point mutation

• After single point mutation, the light-forest may
  be changed.
• The old path is traversed backward from di to s
• The edge we traversed are removed If the use(e)1
  until the following saturations occurred,
• reach s
• reach destination node dl in D which pl is
  assigned to the same wavelength
• reach a node with out-degree gt 1.

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Example of single point mutation
p1s?7 ?1 (10) p3s?9 ?13 ?3 (15) p4s?10 ?4
(8) p5s?10 ?4 ?5 (12)
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Example of single point mutation
p1s?7 ?1 (10) p3s?9 ?13 ?3 (15) p4s?10 ?4
(8) p5s?10 ?4 ?5 (12)
if p5 is mutated to p5s?8?5 then the old path 4
?5 is removed and new path is tested whether is
conflict to current light-tree or not. if no
then assign new path to current
wavelength. otherwise, another light-tree
of different wavelength is tested and selected to
assign.
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Example of single point mutation
p1s?7 ?1 (10) p3s?9 ?13 ?3 (15) p4s?10 ?4
(8) p5s?10 ?4 ?5 (12)
if p4 is mutated to p4s?10?12 ?4 then the old
path 4 ?5 is not removed and new path is tested
whether is conflict to current light-tree or
not. if no then assign new path to current
wavelength. otherwise, another light-tree
of different wavelength is tested and selected to
assign.
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Example of mutation
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Heuristic Initialization

• Farthest First
• To improve the performance of GA.
• Notations
• Edge(P(si,di))
• The set of edges that in path P(s,di) or edges
  that at least one of its endpoints (not s) on
  P(s, di).
• GG-Edge(P(si,di))

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Example

• Edge(P(s,2))(s,7), (7,14), (14,2), (1,7),
  (1,14), (3,14), (2,11), (2,15), (2,16)

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Sub-trees

• Let degree(s) be the degree of the source node s
  on tree P (minimal cost tree).
• PT(vi) be the sub-tree rooted at node vi.

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Properties of sub-tree

• If there are more than one destination on the
  leaves in a sub-tree PT(vi), than violated the
  light-splitting constraint.
• Thus, only one destination node on leaves can be
  chosen to route by this sub-tree and the others
  should be re-routed.
• To determined the rerouting paths of the
  destinations in the leaves, some heuristics are
  proposed.

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Algorithm Farthest-First

• For each sub-tree PT(vi), only the farthest
  destination is routed by the path P(s, di).

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Re-route

• How to re-route?
• The routed paths and nodes used by the farthest
  path in each sub-tree cannot be used twice.
• The re-routing paths together with the exist
  paths can not perform cycle(s) or violated the
  light-splitting constraint.
• EDGE(P(s,v)) in each sub-trees should be removed.

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Remove EDGE(P(s,v))
G
UNREACH 3, 1
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Experimental

• PC Pentium III 1GMHz, 512MB RAM.
• Borland C.
• Windows 2000.

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Result
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Conclusions

• A genetic algorithm is proposed to solve the
  Multicast routing on WDM network.