THE LANDMARK HIERARCHY: A NEW HIERARCHY FOR ROUTING IN VERY LARGE NETWORKS Paul F. Tsuchiya

1. THE LANDMARK HIERARCHY: A NEW HIERARCHY FOR ROUTING IN VERY LARGE NETWORKSPaul F. Tsuchiya Presenter: Saeed ullah

2. Agenda • Introduction • The Area Hierarchy • The Landmark • Hierarchy of Landmarks • Routing in a Landmark Hierarchy • Dynamic Algorithms in Landmark Routing • Static Performance • Summary • Conclusion

3. Introduction • Landmark Routing is a set of algorithms for routing in large communications networks. It is based on a new type of hierarchy, called Landmark Hierarchy. • Landmark Routing has the following features: • operates efficiently and automatically in networks of large size • responds to changing network conditions such as topology changes • provides full name-based addressing • provides automatic address assignment • accommodates administrative boundaries, providing control of routing paths, protection, and autonomy • This paper presents a description of the Landmark Hierarchy and compares it to the Area Hierarchy.

4. The Area Hierarchy • Area Hierarchy is created by logically grouping routers into areas, grouping areas into super-areas, and so on. • Single router in Figure 1 is considered to be a Level 0 area, a group of routers to be a Level 1 area, and a group of Level 1 areas to be a Level 2 area. • Routers outside the area see the area as a single entity. Which means that only one entry is required in that router’s routing table to route to several routers in another area. • The decrease in the size of the routing table causes the increase in the path length.

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6. 1.3.1 1.3.1 1.3.1 1.1.1 1.1.2 1.1.3 1.1.4 3.1.2 1.2.2 1.2 3.1 1.2.1 3.1.3 3.1.1 1.2.3 1.3 3 3.2.4 13.2.3 3.2 1 3.2.2 3.2.1 1.1 2.2.1 2.1.1 2.2.3 2.1.4 2.2 2.2.2 2.1.2 2.1.3 2.1 2

7. 1.3.1 1.3.1 1.3.1 1.1.1 1.1.2 1.1.3 1.1.4 3.1.2 1.2.2 1.2 3.1 1.2.1 3.1.3 3.1.1 1.2.3 1.3 3 3.2.4 13.2.3 3.2 1 3.2.2 3.2.1 1.1 2.2.1 2.1.1 2.2.3 2.1.4 2.2 2.2.2 2.1.2 2.1.3 2.1 2

8. 1.3.1 1.3.1 1.3.1 1.1.1 1.1.2 1.1.3 1.1.4 3.1.2 1.2.2 1.2 3.1 1.2.1 3.1.3 3.1.1 1.2.3 1.3 3 3.2.4 13.2.3 3.2 1 3.2.2 3.2.1 1.1 2.2.1 2.1.1 2.2.3 2.1.4 2.2 2.2.2 2.1.2 2.1.3 2.1 2

9. The Landmark • A Landmark is a router whose neighbor routers within a certain number of hops contain routing entries for that router. • On Figure 2: router 1 is a Landmark which can be ”seen” by all routers within a distance of 2 hops. It is also called a Landmark of radius 2.

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

11. Hierarchy of Landmarks • LMi refers to a Landmark of hierarchy level i, i=O being the lowest level, and i=H being the highest level. • LMi[id] refers to a specific LMi, with label id, called the Landmark ID. • ri[id] is a radius of a corresponding LMi[id]. • In the Landmark Hierarchy, every router in a network is a Landmark LM0[id] of some small radius r0[id].

12. r1 [b] r0 [a] LM0 [a] LM1 [b] LM2 [c] Source

13. Routing in a Landmark Hierarchy • Routing Table • Each router keeps a table of the next hop on the shortest path to each Landmark for which it has routing entries. • Addressing • The address of a router is a series of Landmark IDs of the Landmarks at each hierarchical level which the router is near. • Each Landmark in the address must be within the radius of the Landmark with next lower Landmark ID in the address. • E.g. let’s consider a Landmark Address LM2[c].LM1[b].LM0[a]. LM2[c] is called a parent of LM1[b], and LM1[b] is called a child of LM2[c]. • Routing • Finding a path from the router Source to the router LM0[a].

14. d.d.f d.i.k d.d.e d.i.g d.d.d d.d.a d.i.i d.d.c d.d.j d.d.l d.d.k d.i.w d.d.b d.n.h d.i.u d.n.t d.n.n d.n.x d.i.v d.n.q d.n.s d.n.r d.n.p d.n.o

15. Table 1: Routing Table for Router g of Figure 4

16. d.d.f d.i.k d.d.e d.i.g d.d.d d.d.a d.i.i d.d.c d.d.j d.d.l d.d.k d.i.w d.d.b d.n.h d.i.u d.n.t d.n.n d.n.x d.i.v d.n.q d.n.s d.n.r d.n.p d.n.o

17. d.d.f d.i.k d.d.e d.d.d d.d.a d.i.g d.i.i d.d.c d.d.j d.d.l d.d.k d.i.w d.d.b d.n.h d.i.u d.n.t d.n.n d.n.x d.i.v d.n.q d.n.s d.n.r d.n.p d.n.o

18. d.d.f d.i.k d.d.e d.d.d d.d.a d.i.g d.i.i d.d.c d.d.j d.d.l d.d.k d.d.b d.n.h d.i.u d.n.t d.n.n d.n.x d.i.v d.n.o d.n.q d.n.s d.n.r d.n.p d.i.w

19. d.d.f d.i.k d.d.e d.d.d d.d.a d.i.g d.i.i d.d.c d.d.j d.d.l d.d.k d.d.b d.n.h d.i.u d.n.t d.n.n d.n.x d.i.v d.n.o d.n.q d.n.s d.n.r d.n.p

20. d.d.f d.i.k d.d.e d.d.d d.d.a d.i.g d.i.i d.d.c d.d.j d.d.l d.d.k d.d.b d.n.h d.i.u d.n.t d.n.n d.n.x d.i.v d.n.o d.n.q d.n.s d.n.r d.n.p

21. d.d.f d.i.k d.d.e d.d.d d.d.a d.i.g d.i.i d.d.c d.d.j d.d.l d.d.k d.d.b d.n.h d.i.u d.n.t d.n.n d.n.x d.i.v d.n.o d.n.q d.n.s d.n.r d.n.p

22. d.d.f d.i.k d.d.e d.i.g d.d.d d.d.a d.i.i d.d.c d.d.j d.d.l d.d.k d.d.b d.n.h d.i.u d.n.t d.n.n d.n.x d.i.v d.n.q d.n.s d.n.r d.n.p d.i.w d.n.o

23. Dynamic Algorithms in Landmark Routing • Hierarchy management algorithm • Needed for assigning landmarks and determining their corresponding radii • The hierarchy is built from the bottom up. Each Landmark has 3 or 4 children in steady state. 1 is the minimum number of children, while 7 is the maximum number of children. • Routing algorithm • Needed for discovering Landmarks and for establishing paths to Landmarks. • Must be of the distance-vector type • ---------- (contd.)

24. Dynamic Algorithms in Landmark Routing …… • Every router periodically informs its neighbors of it’s distance to one or several destinations. When the neighbor receives such information, it adds its own distance to its neighbors to the distance it had received and decrements the Landmark radius. The distance to the destination is considered to be smallest of the received distances. And the next hop to the destination is the one over which this shortest distance was received. • Algorithm for binding permanent names or IDs to changing addresses • Assured Destination Binding (ADB)

25. Static Performance • In comparing the Area Hierarchy to the Landmark Hierarchy we are looking at two parameters: • R – the average routing table size • - the increase in the path length over shortest path • Routing tables • The Area Hierarchy: • , where H is the number of hierarchical levels, and N is the number of routers in the network.

26. Static Performance ……… • The Landmark Hierarchy: • - ideal conditions • - realistic estimate • Under ideal conditions the Area Hierarchy can achieve smaller routing tables than the Landmark Hierarchy.

27. Static Performance • ”o” data points show the simulation of the Area Hierarchy • ”x” data data points show the simulation of the Landmark Hierarchy • The Landmark Hierarchy performs better than the Area Hierarchy

28. Static Performance • The performance of the Landmark Hierarchy depends on the r/d ratio, where • ri is the radius of the Landmark • diis the distance from a router to the nearest level i Landmark • The Landmark Hierarchy doesn’t perform well for networks with very small diameters compared to the number of routers.

29. Summary • The Landmark hierarchy has been described. • The Landmark hierarchy is easier to dynamically configure. • Dynamic routing in the Landmark hierarchy is briefly mentioned.

30. Conclusion • The Landmark Hierarchy is a promising alternative routing hierarchy, especially for large networks with rapidly changing topologies.

31. Thanks For your attention