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## The Influence of Network Topology on the Efficiency of QoS Multicast Heuristic Algorithms

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Title: The Influence of Network Topology on the Efficiency of QoS Multicast Heuristic Algorithms

1
The Influence of Network Topology on the
Efficiency of QoS Multicast Heuristic Algorithms
CSNDSP '2006
• Maciej Piechowiak
• Piotr Zwierzykowski
• Poznan University of Technology, Poland
• Institute of Electronics and Telecommunications

2
Outline
1. Network topology model
2. Constrained multicast algorithms
3. Topology generation methods
4. Topology visualization
5. Network parameters
6. Simulation results
7. Conclusions

Communication Systems, Networks and Digital
Signal Processing 2006
3
Outline
1. Network topology model
2. Constrained multicast algorithms
3. Topology generation methods
4. Topology visualization
5. Network parameters
6. Simulation results
7. Conclusions

Communication Systems, Networks and Digital
Signal Processing 2006
4
Network model
• network is represented by a directed, connected
graph N (V,E), where V is a set of nodes and E
• with each link e(u,v) ? E two parameters are
coupled cost C(u,v) and delay D(u,v),
• multicast group is a set of nodes that are
receivers of group traffic G g1,...,gn ? V,
node s is a source for group G,
• multicast tree T(s,G) ? E is a tree rooted in
source node s that includes all members of the
group G.

Communication Systems, Networks and Digital
Signal Processing 2006
5
Minimum Steiner Tree (MST)
N(V,E)
Steiner tree is a good representation for solving
multicast routing problem.
Finding Steiner tree is NP-complete problem.
Heuristic algorithms are most preferable.
Communication Systems, Networks and Digital
Signal Processing 2006
6
Outline
1. Network topology model
2. Constrained multicast algorithms
3. Topology generation methods
4. Topology visualization
5. Network parameters
6. Simulation results
7. Conclusions

Communication Systems, Networks and Digital
Signal Processing 2006
7
Constrained algorithms
Constrained algorithms compute least cost path
(tree) without violating the constraint implied
by the upper bound on delay (?).
subject to
Representative algorithms
• KPP algorithm (Kompella, Pasquale, Polyzos),
• CSPT (Constrained Shortest Path Tree),
• LD (Least Delay).

Communication Systems, Networks and Digital
Signal Processing 2006
8
Outline
1. Network topology model
2. Constrained multicast algorithms
3. Topology generation methods
4. Topology visualization
5. Network parameters
6. Simulation results
7. Conclusions

Communication Systems, Networks and Digital
Signal Processing 2006
9
Waxman method
Probability of edge between u and v
d Euclidean distance between node u and v, L
maximum distance between any two nodes in
graph, ?, ? topology parameters an increase
in ? effects in the increase in the number of
edges decrease ? increases the ratio of
the long edges agaist the short ones.
Communication Systems, Networks and Digital
Signal Processing 2006
10
Barabasi method
Probability that new node u connects to a node v
dV degree of a node belonging to the
network, V set of nodes connected to the
network, ? sum of the outdegrees of the nodes
previously connected.
• incremental growth,
• preferential connectivity.

features
Communication Systems, Networks and Digital
Signal Processing 2006
11
Outline
1. Network topology model
2. Constrained multicast algorithms
3. Topology generation methods
4. Topology visualization
5. Network parameters
6. Simulation results
7. Conclusions

Communication Systems, Networks and Digital
Signal Processing 2006
12
Topology visualization
WAXMAN
BARABASI
n 100, k 200, HS 400
Communication Systems, Networks and Digital
Signal Processing 2006
13
Outline
1. Network topology model
2. Constrained multicast algorithms
3. Topology generation methods
4. Topology visualization
5. Network parameters
6. Simulation results
7. Conclusions

Communication Systems, Networks and Digital
Signal Processing 2006
14
Networks parameters
• number of nodes n, number of links k,
• average node degree (Dav),
• diameter length of the longest shortest-path
between any two nodes,
• hop-diameter shortest paths are computed using
hop counts metric,
• length-diameter shortest paths are computed
using Euclidean distance metric,

Communication Systems, Networks and Digital
Signal Processing 2006
15
Networks parameters
• clustering coefficient proportion of links
between the vertices within its neighbourhood
divided by the number of links that could
possibly exist between them

?(v) neighbourhod of v, kv outdegrees of node
v,
• average clustering coefficient,
• number of multicast nodes m.

Communication Systems, Networks and Digital
Signal Processing 2006
16
Outline
1. Network topology model
2. Constrained multicast algorithms
3. Topology generation methods
4. Topology visualization
5. Network parameters
6. Simulation results
7. Conclusions

Communication Systems, Networks and Digital
Signal Processing 2006
17
Simulation results
(m 10, Dav 4, ? 10)
Communication Systems, Networks and Digital
Signal Processing 2006
18
Simulation results
(n 100, Dav 4, ? 10)
Communication Systems, Networks and Digital
Signal Processing 2006
19
Simulation results
(n 40, m 10, Dav 4, ? 10)
Communication Systems, Networks and Digital
Signal Processing 2006
20
Simulation results
(n 40, m 10, Dav 4, ? 10)
Communication Systems, Networks and Digital
Signal Processing 2006
21
Simulation results
(n 40, m 10, Dav 4, ? 10)
Communication Systems, Networks and Digital
Signal Processing 2006
22
Simulation results
(n 40, m 10, Dav 4, ? 10)
Communication Systems, Networks and Digital
Signal Processing 2006
23
Outline
1. Network topology model
2. Constrained multicast algorithms
3. Topology generation methods
4. Topology visualization
5. Network parameters
6. Simulation results
7. Conclusions

Communication Systems, Networks and Digital
Signal Processing 2006
24
Conclusions
• Literature shows relationship between topology
generation methods and efficiency of routing
algorithm.
• Representative muticast heuristic algorithms were
examined.
• Algorithms were compared using the same network
topologies.
• Algorithms comparison using many network
parameters network parameters influence.

Communication Systems, Networks and Digital
Signal Processing 2006
25
The Influence of Network Topology on the
Efficiency of QoS Multicast Heuristic Algorithms
CSNDSP '2006
• Maciej Piechowiak
• Piotr Zwierzykowski
• Poznan University of Technology, Poland
• Institute of Electronics and Telecommunications

26
KPP algorithm (example)
N(V,E)
T1(V1,E1)
? ? 10
• find minimum spanning tree T1 of G1 for each
(u,v) set and cost C(u,v), and delay D(u,v)
according to cost function fC

Communication Systems, Networks and Digital
Signal Processing 2006
27
KPP algorithm (example)
NS(VS,ES)
? ? 10
• replace edges of the found tree by paths from the
original graph G,
• remove loops using Dijkstra algorithm.

Communication Systems, Networks and Digital
Signal Processing 2006
28
Time complexity
algorithm solving routing problem time complexity
MOSPF least-delay O(N log N)
KMB least-delay O(GN2)
KPP delay-constrained least-cost O(?N3)
CSPT delay-constrained least-cost O(N2) / O(N log N)
DCSP delay-constrained least-cost O(K2N2)
Communication Systems, Networks and Digital
Signal Processing 2006