Multicast Routing

1
Multicast Routing

• Algorithms

2
Outline

• Introduction to Multi-point Communication
• Three approaches to Multi-cast Routing
• Steiner Tree Heuristics
• The MZQ algo
• The SCTF algo
• The Virtual Trunk algo for dynamic routing
• The BSMA algo.
• The KPP algo

3
Multipoint Communication

• Concept Single Source, Multiple Destinations,
  Duplication only at branch points.
• Present Day Support
• Communication satellites.
• e-mail lists, internet news distribution.
• Tomorrow's multimedia applications require
• efficient use of bandwidth.
  
  
  
• near simultaneous delivery.

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Applications Multicast Multi-point

• One to Many
• Video Distribution
• Wide scale Information dissemination.

• Many to Many
• Video Conferencing
• Computer Supported Common Work.
• Distributed interactive simulation.
• Large scale distributed (super)computing.
• Distributed Games

5
Semantics of Multi-point Communication

• Reliability
• are different reliability models required for
  different classes of applications?
• Allowing dynamic join and leave
• session has to be receiver controlled.
• Addressing
• how to address groups at each level?
• Whether and how to identify groups in layers
  above the IP layer?
• Directionality
• one-to-many or many-to-many.
• are the transmitters a subset of the receivers?

6
Requirements of Multipoint Routing Algorithms.

• Support reliable transmission
• link failure should not increase delay or reduce
  resource availability.
• Return optimal routes taking into consideration
• price to be paid (bandwidth consumed)
• end to end delay. (no. of links traversed)
• Minimize network load.
• Avoid loops.
• Avoid traffic concentration on a few links or
  sub-nets.
• Minimize the state stored in routers.

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Multipoint Routing algosPerformance Metrics

• Quality of a tree is judged according to the
  following three dimensions
• Low Delay
• End to end delay between source and receiver
  relative to the shortest unicast path delay.
• Low Cost
• Cost of total bandwidth consumption
• Cost of tree state info
• Light Traffic Concentration
• Maximum number of flows on a unidirectional link.
• How evenly the routes are distributed.

8
Routing Algorithms

• All multi-point services use some kind of a
  distribution tree.
• Multicast trees can be
• Shared across sources. (shared trees)
• Only one tree needs to be established for each
  group, which is shared by all the sources within
  that group.
• Source specific. (shortest path trees).
• A shortest path tree rooted at each sending node
  needs to be established

9
SOURCE BASED MULTIPOINT ROUTINGThe Technique.

• A Source Rooted Shortest Path Tree (SRSPT) algo
• Computes the shortest paths between the source
  and each of the receivers within the group.
• Eliminates duplicate data copies on common links.
• Maintains one SRSPT per sender.
• Concept All receiving nodes compute path towards
  the source independently.
• Used by current day IP multicast protocols as
  applications are still
• small scale.
• local area.

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SOURCE BASED MULTIPOINT ROUTINGMerits vs
Demerits

• Advantages.
• SRSPTs are easy to compute. Use the classic
  unicast routing tables.
• Efficient distributed implementations are
  possible
• Entire global topology not required.
• There can be no loops in the path returned.

• Disadvantages
• Does not minimize total cost of distribution
• Does not scale well.
• One piece of state information per source and per
  group is kept in each router.
• May fail badly if the underlying unicast routing
  is asymmetric.

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SHARED TREE APPROACH OF MULTIPOINT
ROUTINGCharacteristics of Steiner Tree based
algorithms.

• The Minimum Steiner Tree The minimal cost
  subgraph spanning a given subset of nodes in a
  graph.
• The Steiner Tree problem is NP-complete.
• finding the minimum steiner tree in a graph has
  exponential cost.
• The tree designed is undirected.
• solution feasible only for symmetric links.
• Monolithic algorithm.
• has to be run each time group membership changes.

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SHARED TREE APPROACH OF MULTIPOINT
ROUTINGCharacteristics of Steiner Tree based
algorithms.

• The SMT defines an absolute limit on the minimum
  tree cost to serve as a reference for gauging
  the cost-optimality of heuristic alternatives.
• The SMT for all members of a multicast group is
  the same irrespective of the role of sender or
  receiver.
• only one state entry needs to be maintained per
  group.
• it scales well for larger groups.
• The SMT may have unbounded delay.
• Worst case maximum end-to-end path length of a
  SMT can be the longest acyclic path within the
  graph.

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An example of a minimum Steiner Tree
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Mcast group members
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AG 6 AE 5 AD 3 AC 3 AI 8 Shortest
Paths from A total distribution cost 16
AG 8 AE 5 AD 3 AC 3 AI 8 KMB Tree
paths from A total distribution cost13
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SHARED TREE APPROACH OF MULTIPOINT
ROUTINGCharacteristics of Core Based Tree
algorithms.

• Concept
• Use the shortest Path Tree rooted at a node in
  the center of the network
• Steps
• Choose an optimal center for the group. Multiple
  cores can be used for better fault tolerance
  delay characteristics.
• Group members send a join message to the center.
• Intermediate nodes mark interface from which the
  multicast info is received and forward it to the
  center.
• Choose the center to
• minimize max/avg delay for all members on the
  tree.
• Minimize the sum of tree-link costs.

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An example of a core based tree.

• A, B, C multi-cast group members

C
A
B
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SHARED TREE APPROACH OF MULTIPOINT
ROUTINGAdvantages of Core Based Tree algorithms

• Work well with multiple senders/receivers
• state information is stored per group, therefore
  scalable.
• Receiver based approach.
• Supports dynamic group membership with relative
  ease.
• Suitable for sparsely distributed receivers.
• SPTs will not have many common links.
• Do not have the unbounded delay problems of SMTs.
• Simple to implement
• used as the basis of PIM and of The CBT
  interdomain Routing Protocol.

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SHARED TREE APPROACH OF MULTIPOINT
ROUTINGDisadvantages of Core Based Tree
algorithms

• Incur extra delay as compared to the RPF
  approach.
• Suffer from traffic concentration on links
  converging towards the center.
• Choosing the optimal center is an NP complete
  problem.
• Locating the center requires complete knowledge
  of the network topology.

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MULTIPOINT ROUTINGTradeOffs between algos

• Any single tree cannot achieve Minimal Cost and
  Minimal Delay both.
• Shortest Path Trees ? Minimize delay at expense
  of Cost.
• Steiner Minimal Trees ? Minimize cost at expense
  of Delay.
• Between these ? spectrum of different types of
  trees offering different tradeoffs.
• Different strategies to place the routes results
  in different degrees of traffic concentration.

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MULTIPOINT ROUTINGIdeals

• Ideally multicast routing algorithms should
• Compute trees with the desired cost and delay
  characteristics.
• Adapt to dynamic group behavior.
• Algorithm should be incremental (like CBT)
  instead of monolithic (like SMT).
• Maintain properties of the original route.
• Not perturb ongoing data transfers.
• Be receiver driven.

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STEINER TREE HEURISTICSProblem Formulation

• Given graph G (V, E, c)
• V Set of vertices
• E Set of edges.
• c Cost function c E ?Z0 ( Edges ? Non
  Negative Integers)
• Z-Vertices Set of Terminals (sometimes referred
  to as M)
• S-Vertices Set of non-terminals
• TO Initial tree s.
• Q Priority Queue of vertices in the tree.
• Vt Vertices in the tree.
• At Edges in the tree.

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STEINER TREE HEURISTICSPruned Dijkstra
Heuristic (PDH) ---Networks v17 92

• Take an arbitrary node as source.
• Find the single source shortest path tree T for
  graph G using Dijkstras algo.
• Delete from T, all S-vertices of degree 1.

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Dijkstras Shortest Path Algorithm.

• Begin.
• ? v?V,
• add v to set U,
• initialize Distance(v) cost(s, v)
• Distance(s) 0 Remove s from U.
• while U is not empty do
• v ? any member of G with minimum distance.
• Remove v from U.
• For each neighbor w of v, do
• if member(w, U)
• distance(w) min(distance(w), cost(w, v)
  distance(v) )
• Stop.

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STEINER TREE HEURISTICSMatsuyamas Minimum
Cost Path Heuristic (MPH) ---Math Japonica
v24

• Begin
• T1 subtree of G containing one arbitrarily
  chosen Z vertex i .
• k 1
• Zki.
• Determine a Z-vertex i ? Z - Zk closest to Tk
• Construct a tree Tk1 by adding the minimum
  cost path from Tk to i
• k k1.
• If k lt p go-to step2.
• If k p, output Tp as the solution
• Stop.

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Matsuyamas Minimum Cost Path Heuristic
Idea For each iteration while M is not empty
--Pick up that node from M which closest to
the tree built so far.
Data Structure Needed All pair shortest paths
(Floydd Warshalls algo O(n3)a)
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STEINER TREE HEURISTICS KMB - A Fast Algo for
Steiner Trees. ---Acta Informatica 1981

• Output A Stiener Tree Th for G and the
  Z-vertices.
• Step 1 Construct a complete directed distance
  graph G1(V1,E1,c1) from G and Z.
• Step 2 Find the minimum spanning tree T1 of G1.
  (pick any to break ties)
• Step3 Construct a subgraph GS of G by replacing
  each edge in T1 by its corresponding shortest
  path in G. (break ties arbitrarily).
• Step 4 Find the minimum spanning tree TS of GS
  (break ties arbitrarily).
• Step 5 Construct a Steiner tree TH from TS by
  deleting edges in TS if necessary, so that all
  the leaves in TH are Steiner points.
• Worst case time complexity O(SV2).
• Cost no more than 2(1 - 1/l) optimal cost
• where l number of leaves in the steiner tree.

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Working of KMB
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Working of KMB
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Destination Nodes
Intermediate Nodes
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Multicast Tree Generation AlgorithmsThe MZQ
Algorithm for multicasting in all optical
networks -- Malli, Zhang, Qiao

• Limited wavelength conversion every node is
  capable of converting an input wavelength to only
  a subset of output wavelengths.
• Sparse wavelength conversion an input
  wavelength can be converted to any output
  wavelength, but only a few nodes posses this
  capability.
• Sparse Splitting only a fraction of nodes can
  forward as many copies as needed, and the rest of
  the nodes have no splitting capability.
• MZQ assumes there are always enough wavelengths
  on each link.
• Constructs multi-cast trees based on splitting
  capability of the nodes.
• Nodes without splitting capability can have
  at-most one child in the tree.

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Multicast Tree Generation AlgorithmsThe MZQ
Algorithm Routing -- Malli,
Zhang, Qiao

• Algorithm maintains three sets of nodes
• V nodes in the tree through which the tree can
  grow .
• (nodes with splitting capability).
• V nodes in the tree through which the tree
  cannot grow.
• (nodes without splitting capability)
• UV set of Terminals not included in any tree so
  far.
• Pick that node from UV which is nearest to the
  tree
• Include as many destinations as possible in one
  multicasting tree.
• For nodes not included in the preceding tree(s),
  algorithm called recursively to construct another
  multicasting tree.

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Multicast Tree Generation AlgorithmsThe MZQ
Algorithm Wavelength Assignment
-- Malli, Zhang, Qiao

• Performance Metrics
• Number of Wavelengths
• Total amount of Bandwidth (Total number of
  Channels)
• Two counters maintained on each link
• I? highest wavelength index being used.
• N? number of wavelengths being used.
• Unlimited wavelengths on each link.
• First-Fit algorithm used for wavelength
  assignment.

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The MZQ AlgorithmMulticasting forest in a
NSF-NET like network
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Source
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Node with full Splitting Capability
Node with no splitting capability
32
Multicast Tree Generation AlgorithmsThe MZQ
Algorithm for multicasting in all optical
networks -- Malli, Zhang, Qiao

• Results
• The bandwidth savings from using multicasting
  saturate at 50.
• Multicasting reduces number of wavelengths
  required by as much as 60.
• Even when the network does not have any nodes
  that have the splitting capability, multicasting
  reduces the bandwidth consumed by 43 to 45.
• No more than 75 of the nodes need to have the
  splitting capability to obtain the same effect as
  having the splitting capability in all the nodes.

33
Multicast Tree Generation AlgorithmsSCTF-Algo
(Selective Closest Terminal First)
S.
Ramanathan, ---IEEE Infocom 1996

• Initially Tree T source.
• Repeat until M is empty
• Extend one branch from T to a terminal in M.
• remove that terminal from M.
• Stop
• Vertices in Tree are maintained as a priority
  queue with
• priority(source) gt priority(terminals) gt
  priority(non-terminals).
• Bin B holds first ? vertices of the queue.
• Choose the path of least cost from all vertices
  in B to all non-terminals not in the Tree.

34
Multicast Tree Generation AlgorithmsSCTF-Algo
Formal Description.
---IEEE Infocom 1996

• Init Q ? s, Vt ? s,
  At ? .
• While M not empty do
• B ? first min(?? , Q ) vertices in Q.
• Initialize PATH to any path from B to M.
• For each v in B do
• for each m in M do
• if cost( shortestPath( v, m) lt cost (PATH) PATH ?
  P.
• Branch ? subpath ( w ? z ) only w is in Vt.
• Insert vertices in Branch into Q.
• Vt ? Vt ? vertices in Branch , At ? At ?
  edges in Branch.
• M ? M ? terminals in Branch.
• Return T.

35
Multicast Tree Generation AlgorithmsSCTF-Algo
Subsuming three other algorithms
---IEEE Infocom 1996

• PDH, MPH, and KMB are special cases of the
  R-algo.
• ? 1. SCTF equivalent to PDH.
• ? M1 Ignore non-terminals in B.
• SCTF equivalent to KMB.
• ? V. SCTF equivalent to MPH.
• As ? ? from 1 to n, Tree_Cost ?, and Running_Time
  ?.
• Running_Time ? linearly.
• Tree_cost ? very rapidly.
• Low ? good operating point.

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Multicast Tree Generation AlgorithmsR-Algo.
Performance Characteristics
---IEEE Infocom 1996

• Running Time of R-Algo O(m2? e)
• Assumption Shortest Paths from every vertex to
  every terminal are available. ( takes O( m . n .
  log(e) ) time )
• Performance Guarantee
• ?A max A(I)/OPT(I)
• Tree cost ? 2 . ?m. Optimal_Cost
• ?m MAXu, v max(cost(u,v), cost(v, u))/
  min(cost(u,v), cost(v, u))
• ?m 1 for symmetric graphs.
• ?A O ( ?m).

37
Multicast Tree Generation AlgorithmsFeatures of
the SCTF-Algo ---IEEE
Infocom 1996

• Controlling knob ? enables use of the SCTF-algo
  for both
• Delay Optimization. (? 1)
• Cost optimization. (? n)
• Advantageous for MultiMedia applications
• select the right tradeoff operating point to
  accommodate the differing requirements of voice,
  video and data.

38
Multicast Tree Generation AlgorithmsVTDM - A
Dynamic Multicast Routing Algorithm H.C.Lin
S.C. Lai ---IEEE Infocom 1998

• Problem Formulation..
• Source node s.
• Sequence of requests R r1, r2, ... rm
• Each request ri either adds a destination node to
  
• or removes a destination from the multicast
  group.
• The DMRP Find a sequence of multicast trees
• Ti, i 1 .. m such that certain overall cost
  is minimum.
• This does not allow re-routing of existing
  connections as the sequence of requests proceeds.
  

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Cost Modelling

• w(e, ?i ) Cost of using wavelength ?i on edge e.
• Infinite if ?i is not available on edge e.
• cv(?p , ?q ) Cost of wavelength conversion at
  node v, from ?p to ?q .
• Infinite if ?p cannot be converted to ?q at node
  v.
• If p q, then cv(?p , ?q ) is zero.
• C(T) ?v ?T w(p(v), v), ?(v))
• ?v ? T-s C p(v) (? (p(v)), ?(v))
• where p(v) means parent of v in the tree.

40
The VTDM algo Concept of a Virtual Trunk
---Infocom 1998

• A virtual trunk is a tree of the underlying
  graph.
• Spans nodes which have the greatest probability
  of being a part of the multi-casting tree.
• Used as a template for building the multicasting
  tree.
• Nodes which have a greater number of shortest
  paths passing through them, have a greater
  probability of being a part of the multi-cast
  tree.
• Weight W(vi) of vertex vi number of shortest
  paths passing through vi.

41
The VTDM algo Building the Virtual Trunk
---Infocom 1998

• Find the shortest paths for all pairs of nodes in
  G.
• Assign weights to the vertices in G.
• Find the set of trunk nodes F.
• Construct a complete graph for the set of trunk
  nodes.
• Find the minimum spanning tree for the complete
  graph.
• Convert edges in min. span. Tree back to the
  corres shortest paths in graph G.
• Run the minimum spanning tree algo and remove
  unnecessary nodes and links to obtain the virtual
  trunk.

42
The VTDM algo The VTDM routing algorithm
---Infocom 1998

• Build the virtual trunk.
• Adding a node to the multicast group
• establish shortest route from the node to the
  virtual trunk. is established.
• Route along virtual trunk to source node also
  established if not yet there.
• Add node to the multicast group.
• Removing a node from the multi-cast group
• First remove the node from the multicast group.
• If it is a leaf node, remove the node from the
  tree.
• Prune the excess branch, if the node did not have
  any downstream nodes.

43
The VTDM algo Node Addition (adding node
B) ---Infocom 1998

• Step1
• If node B on the virtual trunk, denote it as node
  A go to step2.
• Else, find the shortest route from node B to the
  virtual trunk.
  
• Add portion of the shortest route not yet
  included in the multicast tree to the multicast
  tree.
  
  
• Let node A be the node on the virtual trunk which
  attaches node B to the virtual trunk via the
  selected shortest route.
• Step2
• If node A is already on the multicast tree go to
  step 3.
• Else add portion of route from node A to source
  node that has not yet been included in the
  multicast tree to the multicast tree.
• Step3
• Add node B to the multicast group.

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The VTDM algo Node Removal (removing node
B) ---Infocom 1998

• Step1
• Remove node B from the multicast group.
• Step2
• If node B has downstream nodes the procedure is
  done.
• Else, if node B is a leaf, remove node B and its
  upstream link to the multicast tree.
• Step3
• If the upstream node of node B is in the
  multicast group, the
  procedure is done.
• Else denote this node as node B and go to step 2.

45
The VTDM algo Simulation Results
---Infocom 1998

• Mean Inefficiency TreeCost using AlgoA/
  TreeCost using AlgoB.
• KMB is taken as the reference algorithm.
• VTDM compared against dynamic greedy (DG),
  Shortest Path (SP).
• Mean Inefficiency versus Number of nodes
• significant improvement over SP, better than DG.
• Mean Inefficiency versus Size of multicast group.
• significant improvement over SP, better than DG
  for large grps.
• Max Degree of nodes in the multicast trees. (no.
  of data copies).
• Much lesser degree than SP, less than DG
  algorithm.

46
Multicast Tree Generation AlgorithmsBSMA -
Bounded Shortest Multicast Algorithm Zhu,
Parsa Aceves---IEEE Infocom 1995

• Problem
• Minimize the tree cost.
• Guarantee all delays are less than predetermined
  bounds.
• Feasible region
• the set of all delay bounded Steiner trees.
• Steps
• Construct minimum delay steiner tree T0 using
  Dijkstras shortest path algorithm
• Refine T0 iteratively for lower cost while
  staying within feasible region.

47
Multicast Tree Generation AlgorithmsBSMA -
Definition of the cost function.
---IEEE Infocom 1995

• Utilization Driven Cost
• Minimizes sum of link costs along the path.
• Congestion Driven Cost
• Minimizes maximal link cost requirement along
  paths.
• Link cost function
• Cost of the link associated with the utilization
  of the link.
• Link delay function
• Queuing, Transmission, and Propagation delays on
  the link.
• Destination Delay Bound Function (DDF)
• Upper bound to the delay along path from the
  source to each of the destinations.

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Multicast Tree Generation AlgorithmsBSMA -
Refinement of the tree for lower costs.
---IEEE Infocom 1995

• Path Switching
• refinement of Tj to Tj1.
• Choosing a path p to be taken out of Tj.
• Tj Tj1 Tj2 ? p
• Choosing the new path ps in G not in Tj that
  replaces the path to be deleted from Tj.
• Tj1 Tj1 Tj2 ? ps. Tj1 is delay bounded.

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Multicast Tree Generation AlgorithmsBSMA -
Refinement of the tree for lower costs.
---IEEE Infocom 1995

• From Tj get Tj/.
• Tj/ has the source, all destination nodes, and
  all relay nodes of degree more than 2.
• Tj/. Edges of Tj/ are called super_edges.
• All nodes between the two end_nodes of a
  super_edge are relay nodes of degree 1.
• Every super_edge represents a candidate path in
  Tj for switching.

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Multicast Tree Generation AlgorithmsBSMA -
Algorithm Details
---IEEE Infocom 1995

• Initially all super_edges are unmarked.
• Step1Among all unmarked super_edges, BSMA
  selects the super_edge Ph with the highest
  path cost.
• Exchange it with another super_edge of lesser
  cost, such that resulting tree is delay bounded..
• One of the two cases must happen
• The delay bounded shortest path is the same as
  Ph.
• Mark that super edge. Go to Step1.
• The delay bounded shortest path is a path other
  than Ph.
• Do The replacement.
• Unmark all super_edges.
• Go to Step 1.
• Stops when all super edges are marked.

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Multicast Tree Generation AlgorithmsBSMA -
Algorithm Details
---IEEE Infocom 1995

• BSMA incrementally calculates k shortest paths
  between subtrees Tj1 and Tj2.
• K is determined only after a shortest path is
  found which has resulted in a delay bounded tree.
  So the shortest path incremental construction
  stops when one of the following two conditions is
  satisfied.
• The shortest path found does not result in the
  new tree violating the delay bound.
• The shortest path found has equal path length
  to the one just deleted.
• Dijkstras algo is extended to construct shortest
  path between two subtrees instead of two nodes
• A pseudo source node s is connected to all nodes
  in Tj1 and a pseudo destination node d is
  connected to all nodes in Tj2.
• The shortest path algo starts from s and ends at
  d.

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The BSMA algo cont
6,2
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The BSMA algo Greedy Path switching ---IE
EE Infocom 95

• Gain cost reduction after a round of path
  switching
• if c cost of Tj and c_prime cost of Tj1,
  then
  gain c - c_prime.
• BSMA computes gains of all pairs of possible path
  switchings in Tj and then selects one with the
  maximum gain.
• BSMA continues the greedy switching and
  terminates when the maximum gain is zero.
• The time complexity of this greedy approach is
  more.

54
The BSMA algo Simulation Results

• Time complexity of BSMA O(kn3log(n)).
• Using the tightest possible delay bound, as
  determined by the min. delay tree, the cost of
  the BSMA tree is substantially better than the
  cost of the min. delay tree.
• A Range of min. cost solutions can be obtained
  between the two extremes of the KMB and the min.
  delay solution.
• Compared to KMB the relative quality of results
  improve with the number of destinations in the
  multicast group.
• A tighter bound results in a larger value for k,
  and hence increases the computation time required
  by the algo, a slight relaxation of the bound
  often results in considerably fewer computations.

55
Multicast Tree Generation AlgorithmsKPP
algorithm for a delay constrained Steiner Tree
Kompella,
Pasquale, Polyzos ---IEEE Infocom 1995

• Problem
• Minimize the tree cost. is
  minimized.
• Bounded end-to-end delay.
• Features
• Edge_Cost and Delay are different functions.
• Delay constraints are on individual path delay.
• Assumption
• Source has all the info necessary for tree
  construction.

56
Multicast Tree Generation AlgorithmsKPP
algorithm for a delay constrained Steiner Tree

---IEEE Infocom 1995

• Constrained Cheapest Path between v and w
• Least cost path between v and w that has delay
  less than ?.
• Cost of such a path is PC(v, w).
• Delay on this path is PD(v, w).
• Closure graph G/
• A complete graph on the nodes in N, with PC(v,
  w) as edge costs PD(v, w) as the edge delay.
• To compute Closure graph G/
• Calculate all-pair-constrained-cheapest-paths
  using Floyds
• algorithm. (? is bounded, so possible in
  poly-time)

57
Multicast Tree Generation AlgorithmsKPP
algorithm details

---IEEE Infocom 1995

• Cd(v, w) minu?V Cd-D(u, w)(v, u) C(u, w)
• Cost of cheapest path from v to w with delay
  exactly d.
• PC(v, w) min dlt? Cd(v, w)
• Compute all-pair-constrained-cheapest-paths.
• From these, compute G/.
• Constructing graph G/ takes O(n3 ? ) time.

58
Multicast Tree Generation AlgorithmsKPP
algorithm details

---IEEE Infocom 1995

• Compute the closure graph G/ of G.
• Construct a constrained spanning tree T/of G/,
  using one of the two selection functions fC or
  fCD as the selection function.
• Expand the edges in the constrained spanning tree
  T/ into the constrained cheapest paths they
  represent, and remove any loops that may be
  caused by this expansion.

59
Multicast Tree Generation AlgorithmsKPP
algorithm - Two Source Based Heuristics

---IEEE Infocom 1995

• CSTCD
• Tries to choose low cost edges but modulates the
  choice to pick edges that maximize the residual
  delay.
• This increases the chances of extending the path
  along this edge, and beyond to another
  destination.
• Has a tendency to optimize on delay.
• May find trees with delay far lower than ? at the
  expense of added cost to the tree.
• Uses fCD if P(v) D(v, w)
  lt ?
• fCD infinity otherwise

60
Multicast Tree Generation AlgorithmsKPP
algorithm - Two Source Based Heuristics

---IEEE Infocom 1995

• CSTC
• minimizes fC.
• Constructs cheapest tree possible, while
  remaining within delay bounds.
• Minimizes cost, without unduly minimizing delay.
• fc C(v, w) if P(v) D(v, w) lt
• fc infinity otherwise.

61
Multicast Tree Generation AlgorithmsKPP
algorithm - Performance Evaluation.

---IEEE Infocom 1995

• CSTC and OPT have comparable performance.
• CSTCD performs marginally worse than CSTC.
• For large group sizes the heuristics converge to
  the optimal solution.
• When delay-tolerance increases, the performance
  of both source based heuristics converges.
• SPT gives trees with consistently high costs
  (70-80) more than CSTC.

62
List of References

• KMB Algorithm L Kou, G Markowski, L. Berman
• A Fast algorithm for Steiner Trees.
• Acta Informatica 15, 1981, pages 141-145
• Minimum Cost Path Heuristic H. Takahashi and A.
  Matsuyama
• An Approximate Solution for Steiner Problem in
  Graphs
• Math Japonica vol 24, pp 573-577.
• MZQ Rajkumar Malli, Xijun Zhang, Chunming Qiao
• Benefit of Multicasting in All-Optical Networks.
• SCTF S. Ramanathan
• Multicast Tree Generation in Networks with
  Asymmetric Links.
• IEEE/ACM Transactions on Networking 1996 v4,
  558-568

63
List of References .continued

• BSMA Qing Zhu, Mehrdad Parsa, J.J.
  Gracia-Luna-Aceves
• A source based algo. for delay constrained
  minimum cost multicasting.
• IEEE Infocom 1995 pp 377-385
• VTDM Hwa-Chun Lin Shou-Chuan Lai
• A dynamic Multicast Routing Algorithm
• IEEE Infocom 1998, pp 1426-1432
• KPP V. P. Kompella, J. C. Pasquale, G. C.
  Polyzos
• Multicast Routing for Multimedia Communication.
• IEEE /ACM Transactions on Networking, vol 1,
  June 1993.