UCDavis SecLab MURI October 20022

Outline Part 1

• Application to OSPF routing protocol• Augmented OSPF• Betweenness centrality computation• Sample Topology• Ongoing work


Application to OSPF Routing

• OSPF NOW

– At each router participating in OSPF Link-State Routing, the router employs the Dijkstra SPF Alg. and determines the shortest path tree originating at that router

– Every link update received by router results in SPF algorithm execution

– Employing a Fibonacci heap sort, algorithm executes in O(e+nlog(n)) time for e edges and n nodes


• OSPF AUGMENTED

– Modified Definition of Betweenness Centrality:

Centrality of a node is determined with

respect to root router of SPF tree

– Advantages• Each router independently computes

betweenness centrality indices of other routers in its routing network

• Each router can adopt independent response decisions based on this metric


• Betweenness Centrality Computation

– Piggyback betweenness centrality computation within Dijkstra SPF algorithm at each router executing OSPF, for all routers in the routing network

– Order of computational time requirements for

determining this index remain UNCHANGED from

existing Dijkstra computation, i.e., O(e+nlogn) at each router


Augmented Dijkstra’s SPF Algorithm

Given a graph with n nodes, find a shortest path tree from source node SS = Source nodeE = set of evaluated nodes for which shortest paths are knownR = set of remaining nodes, ViO = ordered list of pathsC_B(V_i), i = 1,.., n /* Centrality index of all nodes, V_i, with respect to source node, S */

• Step 1 C_B(V_i) = 0 E = {S} R = {V_1, V_2, …, V_(n-1)} O = {set of 1-edge paths starting from S} = {P_1, P_2, …, P_i} /* Each path has a cost corresponding to the link metric, and the paths are sorted by increasing metrics */

• Step 2 if O = Ø or if metric(P_1) = ∞ /* All paths have been considered, or the first path has infinite metric */ mark all remaining nodes in R as unreachable Terminate algorithm contd


Augmented Dijkstra’s SPF Algorithm – contd.

• Step 3

Let V = last node in P_1

If V Є E , go to Step 2

else P_1 is the shortest path to V

Move V from R to E

Increment C_B(V_i) for all V_i Є path P_1, where V_i ≠ S or V /* Centrality index is

incremented for all nodes

in the path between

S and V */

• Step 4

Build new set of paths by concatenating P_1 with each of the new edges from V

Cost of the new paths = cost of P + link metric of new edge

Insert new links in O, while sorting O

Go to Step 2


D

EFG 2

A B C2 43

2

2

1 3 6

D

EFG 2

A B C2 43

2

2

1 3 6

D

EFG 2

A B C2 43

2

2

1 3 6

Initial Network Topology

Topology after Link FE fails

Topology after Link GF fails


B C D E F G

1 0 0 1 2 3

3 2 1 0 0 1

4 2 1 0 0 0

+3 +2 +1 -1 -2 -3

G

EC

B

A

D

F

1. Initial SPF tree

F

G

E

C

B

A

D

3. Link GF Failure

F

E

G

C

B

A

D

2. Link FE Failure

Nodes

Initial Betweeness Centrality C_B of Node

C_B after link FE failure

C_B after link GF failure

Change in C_B after 2 link updates

Initial Degree Centrality C_D of Node 3 3 2 3 3 2

Change in C_D after 2 link updates 0 0 0 -1 -2 -1

Node B has more control of the network Node F is more isolated


• Ongoing Work

– Augmented current link-state algorithm (rtProtoLS) implemented in network simulator, ns-2, to incorporate centrality computations and perform comparative performance analysis on this augmented algorithm

– Running simulations on ns-2 for realistic network scenarios to test validity of centrality indices for various cases of spatial and temporal as well as random and correlated link failures


Outline Part 2 : Simulation Results

• Requirements of betweenness centrality calculation

• Simulator choice and reasons• Test topologies and derived results• Issues with simulation• Conclusion


Requirements of betweeness centrality calculation

• Need to maintain state of all the shortest paths from a given node.All hops along the path need to be maintained to calculate their betweenness

• An efficient method of calculation of the centralitypiggybacking of calculation on shortest path calculation


NS

• Reasons used– In-house expertise– An implementation of linkstate available– A popular simulator among networking

researchers– Proof of concept prototype development

• Open to use of any suitable simulator for future work


Topology 1

• 23 nodes• All links are duplex• Cost of links between

node 0 – node 1 : 10

node 4 – node 5 : 10

node 2 – node 3 : variable

All other links cost : 1


Topology 1


Results Topology 1

View of Centrality from node 11

0

2

4

6

8

10

12

14

1 2 3 4 5 6 7 8 9 10 11 12

Cost of Link b/w node 3 and node 2

Cen

tra

lity

Node 1Node 3


Topology 2


Results Topology 2

Centrality of Node 3

0

2

4

6

8

10

12

14

1 2 3 4 5 6 7 8 9 10

cost of links from node 3

cent

ralit

y

node 11


Topolgy 3

• 24 nodes• All links duplex• Cost of links between node pairs

(2,3) (3,5) (2,4) (4,5) (0,2) (13,16): 2

(9,19) : 6

(0,1) : variable

All other links cost : 1


Topology 3


Results Topology 3

Centrality of Node 7 from Node 14 and 17 when link 0-1 changes cost

0

2

4

6

8

1 2 3 4 5 6 7 8 9

cost of link between nodes 0-1

cent

ralit

y no

de 7

Node 14Node 17


Issues With NS

• Linkstate documentation non-existent• Extensive use of STL makes linkstate

inefficient• State for the paths not maintained


Other Issues

• Stable view of OSPF centrality is difficult to obtain : heuristic needed to determine the stability of the centrality

• Method of dealing with multiple equal shortest paths needed


Conclusion

• Demonstrated that the betweenness centrality index is an important metric for security and traffic flow.

• Can be calculated by piggybacking onto the calculation of the OSPF shortest path.


Contact Information

• Akshay Aggarwal

[email protected]

• Poornima Balasubramanyam

[email protected]

intrusion monitoring of link-state routing protocols

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