An efficient algorithm for group multicast routing with bandwidth reservation

1
An efficient algorithm for group multicast
routing with bandwidth reservation

• C.P. Low, N. Wang
• Computer Communications 23 (2000) 1740-1746
• Presented by Tzu-Cheng Hsieh, OPLab, IM, NTU
• 2007/5/21

2
Agenda

• Introduction
• Lemma
• Previous work (Jia and Wangs algorithm)
• The new proposed algorithm
• Simulations
• Conclusion and future work

3
Agenda

• Introduction
• Lemma
• Previous work (Jia and Wangs algorithm)
• The new proposed algorithm
• Simulations
• Conclusion and future work

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Introduction (1/3)

• Group multicasting is a generalization of
  multicasting whereby each member node from a
  group may multicast data to all other members
  from the same group, i.e. each member node being
  both an information source and destination.
• It can be easily inferred that group multicasting
  will need higher bandwidth resources than the
  corresponding single source multicast routing.

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Introduction (2/3)

• Jia and Wang have proposed a group multicast
  routing algorithm that is based on an adaptation
  of Kou, Markowsky and Bermans (KMB) algorithm.
• Empirical studies have shown that the Takahashi
  and Matsuyama (TM) Steiner tree heuristic
  produces better overall cost performance than the
  KMB heuristic for constructing single source
  multicast trees.

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Introduction (3/3)

• In this paper, we propose an algorithm that is
  based on the adaptation of algorithm by TM for
  group multicast routing.
• Extensive simulations are carried out to compare
  the performance of our proposed algorithm with
  the algorithm that was proposed by Jia and Wang,
  which we will refer to as Jia and Wang's
  algorithm.

7
Agenda

• Introduction
• Lemma
• Previous work (Jia and Wangs algorithm)
• The new proposed algorithm
• Simulations
• Conclusion and future work

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Lemma (1/2)

• Lemma 1 There is no feasible solution for GMRP
  (group multicast routing problem) if
• (i) all member nodes do not belong to the
  same connected component or
• (ii) the total input bandwidth for some
  member node v is less than k-1 (k is the amount
  of the group members).
• Lemma 1 can be used as an early-abort test to
  determine in advance if a feasible solution
  exists before attempting to find any solutions
  for GMRP.

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Lemma (2/2)

• An edge is said to be saturated if the difference
  between its available bandwidth and its allocated
  bandwidth is less than the amount of bandwidth
  required by a user.

10
Agenda

• Introduction
• Lemma
• Previous work (Jia and Wangs algorithm)
• The new proposed algorithm
• Simulations
• Conclusion and future work

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Previous work (Jia and Wangs algorithm) (1/7)

• We observe that generating a set of trees
  separately, with any coordination, for GMRP is
  likely to result in solutions with higher cost.
• This is due to the fact that earlier choices of
  links in the process of generating a set of trees
  may force trees which are generated later to
  choose links that results in higher cost overall
  solution.

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Previous work (Jia and Wangs algorithm) (2/7)

• Jia and Wang's algorithm, for GMRP adopts some
  form of coordinated strategy to generate a set of
  multicast trees.
• Their algorithm is based on an adaptation of the
  KMB Steiner tree heuristic.

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Previous work (Jia and Wangs algorithm) (3/7)

• KMB's algorithm begins by computing shortest
  paths between each pair of member nodes.
• Following that, the closure graph G which
  contains only nodes in member group D is
  constructed.
• The next step is to construct a spanning tree of
  G.

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Previous work (Jia and Wangs algorithm) (4/7)
1
5
34
34
5
31
25
12
25
25
12
22
39
0
3
10
10
9
20
9
20
30
17
30
30
17
30
2
4
13
13
4
The cost of the resultant tree is 77
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Previous work (Jia and Wangs algorithm) (5/7)

• When two or more trees compete for a saturated
  link, it would simply imply that some of these
  trees would have to use alternative links to get
  to the other member nodes in the trees.
• The difference in cost between the original tree
  and the alternative tree is known as the
  alternative overhead.
• The tree with the least alternative overhead will
  be forced to give up this link and take the
  alternative link.

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Previous work (Jia and Wangs algorithm) (6/7)

• Observe that Jia and Wang's algorithm, which is
  based on KMB's algorithm, only considers the
  shortest paths between the member nodes in D in
  the construction of each multicast trees.
• We note there exists another set of shortest
  paths, namely those between the member nodes and
  relay nodes that are not explored by Jia and
  Wang's algorithm.
• The consideration of this additional set of
  shortest paths could possibly lead to lower cost
  solutions for GMRP.

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Previous work (Jia and Wangs algorithm) (7/7)
1
5
34
25
12
0
3
10
9
20
17
30
2
4
13
The cost of the resultant tree is 69
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Agenda

• Introduction
• Lemma
• Previous work (Jia and Wangs algorithm)
• The new proposed algorithm
• Simulations
• Conclusion and future work

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The new proposed algorithm (1/6)

• We will propose a new heuristic algorithm that
  will examine both set of shortest paths mentioned
  above.
• Our proposed algorithm is based on an adaptation
  of the TM Steiner tree algorithm and we call this
  algorithm the Group TM algorithm (GTM).

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The new proposed algorithm (2/6)

• In the TM algorithm, a set V is first
  initialized to contain only the root node.
• The algorithm builds a Steiner tree T(V, E) by
  adding nodes from the member group D to V, one
  at a time, and stops when V contains all nodes
  from D.

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The new proposed algorithm (3/6)

• At each step, it examines all the nodes that
  belong to D but are not in V, and selects the
  one nearest (in terms of cost) to the set of
  nodes in V.
• All nodes along this path are then included in V
  and the edges along the path are added to E.

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The new proposed algorithm (4/6)

• When saturated edges occurs in a tree Tv (rooted
  at v for each v?D), the alternative overhead of
  the current tree Tv is compared with the
  alternative overhead of the most recently built
  tree (or trees) that uses the saturated edges.
• The party that has the smaller alternative
  overhead will have to give up the saturated edges
  and use alternative links to get to other member
  nodes of D.

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1
5
34
6
3
2
25
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1
4
1
0
9
20
20
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2
1
2
2
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15
4
13
5
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Tree 0
Tree 1
Tree 2
C37
C37
C37
1
1
1
0
0
-1
0
0
0
9
9
9
3
2
2
1
0
-1
4
2
15
4
2
15
4
2
15
13
3
13
3
13
3
5
2
5
1
4
1
Tree 0
Tree 1
Tree 2
C47
C47
C79
AO42
AO10
AO10
5
6
2
2
1
1
5
5
1
34
25
25
25
3
2
2
0
0
0
0
0
0
20
9
9
2
2
1
4
2
4
2
2
13
13
5
2
5
0
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The new proposed algorithm (6/6)

• The time complexity of GTM is O(k3n2)

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Agenda

• Introduction
• Lemma
• Previous work (Jia and Wangs algorithm)
• The new proposed algorithm
• Simulations
• Conclusion and future work

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Simulations (1/2)
Network size 100 Mean bandwidth 25
8
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Simulations (2/2)
Network size 100 Member group size 25
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Agenda

• Introduction
• Lemma
• Previous work (Jia and Wangs algorithm)
• The new proposed algorithm
• Simulations
• Conclusion and future work

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Conclusion and future work (1/3)

• In this paper we examine the problem of
  constructing minimum cost group multicast trees
  with bandwidth reservations.
• We provide two criteria, which could be used to
  quickly determine if there exists any feasible
  solution for GMRP.
• Following that we propose a new efficient
  heuristic algorithm, called GTM, for finding low
  cost solutions for GMRP.

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Conclusion and future work (2/3)

• Results from our empirical study show that our
  proposed algorithm performs better in terms of
  cost as compared to Jia and Wang's algorithm.
• In addition, our simulation results also show
  that our proposed algorithm has a higher
  percentage of success in finding solutions for
  GMRP as compared to Jia and Wang's algorithm.

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Conclusion and future work (3/3)

• One possible future research direction is to
  extend the algorithm to handle dynamic group
  membership in which new member nodes may be
  allowed to join the group and existing member
  nodes may leave the group.
• Another future research direction is to extend
  the algorithm to the problem of constructing
  group multicast trees with other QoS constraints
  such as end-to-end delay and delay variations.

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• The End.
• Thanks for your listening!