THE LANDMARK HIERARCHY:THE LANDMARK HIERARCHY: A NEW HIERARCHY FOR ROUTING IN A NEW HIERARCHY FOR ROUTING IN

VERY LARGE NETWORKSVERY LARGE NETWORKS

Paul F. TsuchiyaPaul F. Tsuchiya

Presenter:Presenter:

Saeed ullahSaeed ullah

22

AgendaAgenda IntroductionIntroduction The Area HierarchyThe Area Hierarchy The LandmarkThe Landmark Hierarchy of Landmarks Hierarchy of Landmarks Routing in a Landmark HierarchyRouting in a Landmark Hierarchy Dynamic Algorithms in Landmark RoutingDynamic Algorithms in Landmark Routing Static PerformanceStatic Performance SummarySummary ConclusionConclusion

33

IntroductionIntroduction Landmark Routing is a set of algorithms for routing in Landmark Routing is a set of algorithms for routing in

large communications networks. It is based on a new large communications networks. It is based on a new type of hierarchy, called Landmark Hierarchy.type of hierarchy, called Landmark Hierarchy.

Landmark Routing has the following features: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.

44

The Area HierarchyThe 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.

55

1.3.1

1.3.1

1.3.1

2.2.2

2.2.1

2.2.3

3.1.1

3.1.2

3.1.31.2.1

1.2.2

1.2.3

1.1.1

1.1.3

1.1.4

1.1.2

2.1.1

2.1.2 2.1.3

2.1.4

3.2.4

3.2.1

3.2.2

13.2.3

2

3

1

2.1

1.1

1.3

1.2

2.2

3.2

3.1

66

1.3.1

1.3.1

1.3.1

2.2.2

2.2.1

2.2.3

3.1.1

3.1.2

3.1.31.2.1

1.2.2

1.2.3

1.1.1

1.1.3

1.1.4

1.1.2

2.1.1

2.1.2 2.1.3

2.1.4

3.2.4

3.2.1

3.2.2

13.2.3

2

3

1

2.1

1.1

1.3

1.2

2.2

3.2

3.1

77

1.3.1

1.3.1

1.3.1

2.2.2

2.2.1

2.2.3

3.1.1

3.1.2

3.1.3

1.1.1

1.1.3

1.1.4

1.1.2

2.1.1

2.1.2 2.1.3

2.1.4

3.2.4

3.2.1

3.2.2

13.2.3

2

3

1

2.1

1.1

1.3

1.2.1

1.2.2

1.2.3

1.2

2.2

3.2

3.1

88

1.3.1

1.3.1

1.3.1

2.2.2

2.2.1

2.2.3

3.1.1

3.1.2

3.1.31.2.1

1.2.2

1.2.3

1.1.1

1.1.3

1.1.4

1.1.2

2.1.1

2.1.2 2.1.3

2.1.4

3.2.4

3.2.1

3.2.2

13.2.3

2

3

1

2.1

1.1

1.3

1.2

2.2

3.2

3.1

99

The LandmarkThe 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.

1010

3

12

4

10

11

5

89

6

7

1111

Hierarchy of LandmarksHierarchy 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].

1212

r1 [b]

LM1 [b]

LM2 [c]

r0 [a] LM0 [a]

Source

1313

Routing in a Landmark Routing in a Landmark HierarchyHierarchy Routing TableRouting Table

Each router keeps a table of the next hop on the shortest path to each Landmark for which it has routing entries.

AddressingAddressing 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].

RoutingRouting Finding a path from the router Source to the router LM0[a].

1414

d.d.f

d.i.k

d.i.g

d.i.u

d.d.j

d.d.e

d.i.w

d.i.i

d.n.s

d.i.v

d.n.rd.n.q

d.n.pd.n.o

d.n.h

d.d.c

d.d.b

d.n.n

d.d.a

d.d.k

d.n.x

d.n.t

d.d.l

d.d.d

1515

Table 1: Routing Table for Router g of Figure 4

1616

d.d.f

d.i.k

d.i.g

d.i.u

d.d.j

d.d.e

d.i.w

d.i.i

d.n.s

d.i.v

d.n.rd.n.q

d.n.pd.n.o

d.n.h

d.d.c

d.d.b

d.n.n

d.d.a

d.d.k

d.n.x

d.n.t

d.d.l

d.d.d

1717

d.d.f

d.i.k

d.i.g

d.i.u

d.d.j

d.d.e

d.i.w

d.i.i

d.n.s

d.i.v

d.n.rd.n.q

d.n.pd.n.o

d.n.h

d.d.c

d.d.b

d.n.n

d.d.a

d.d.k

d.n.x

d.n.t

d.d.l

d.d.d

1818

d.i.w

d.n.o

d.d.f

d.i.k

d.i.g

d.i.u

d.d.j

d.d.e

d.i.i

d.n.s

d.i.v

d.n.rd.n.q

d.n.p

d.n.h

d.d.c

d.d.b

d.n.n

d.d.a

d.d.k

d.n.x

d.n.t

d.d.l

d.d.d

1919

d.d.f

d.i.k

d.i.g

d.i.u

d.d.j

d.d.e

d.i.i

d.n.s

d.i.v

d.n.rd.n.q

d.n.p

d.n.h

d.d.c

d.d.b

d.n.n

d.d.a

d.d.k

d.n.x

d.n.t

d.d.l

d.d.d

d.n.o

2020

d.d.f

d.i.k

d.i.g

d.i.u

d.d.j

d.d.e

d.i.i

d.n.s

d.i.v

d.n.rd.n.q

d.n.p

d.n.h

d.d.c

d.d.b

d.n.n

d.d.a

d.d.k

d.n.x

d.n.t

d.d.l

d.d.d

d.n.o

2121

d.d.f

d.i.k

d.i.g

d.i.u

d.d.j

d.d.e

d.i.i

d.n.s

d.i.v

d.n.rd.n.q

d.n.p

d.n.h

d.d.c

d.d.b

d.n.n

d.d.a

d.d.k

d.n.x

d.n.t

d.d.l

d.d.d

d.n.o

2222

d.i.w

d.n.o

d.d.f

d.i.k

d.i.g

d.i.u

d.d.j

d.d.e

d.i.i

d.n.s

d.i.v

d.n.rd.n.q

d.n.p

d.n.h

d.d.c

d.d.b

d.n.n

d.d.a

d.d.k

d.n.x

d.n.t

d.d.l

d.d.d

2323

Dynamic Algorithms in Dynamic Algorithms in Landmark RoutingLandmark Routing

Hierarchy management algorithmHierarchy 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.)

2424

Dynamic Algorithms in Dynamic Algorithms in Landmark Landmark

Routing ……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)

2525

Static PerformanceStatic Performance In comparing the Area Hierarchy to the Landmark In comparing the Area Hierarchy to the Landmark

Hierarchy we are looking at two parametersHierarchy we are looking at two parameters:: R R –– the average routing table size the average routing table size - the increase in the path length over shortest path- the increase in the path length over shortest path

Routing tablesRouting tables The Area Hierarchy:

, where H is the number of hierarchical levels,

and N is the number of routers in the network.

2626

Static Performance ………Static Performance ………

The Landmark Hierarchy:

- ideal conditions

- realistic estimate Under ideal conditions the Area

Hierarchy can achieve smaller routing tables than the Landmark Hierarchy.

2727

Static PerformanceStatic 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

2828

Static PerformanceStatic Performance The performance of the The performance of the

Landmark Hierarchy Landmark Hierarchy depends on the rdepends on the r/d /d ratio, ratio, wherewhere ri is the radius of the Landmark di is the distance from a router

to the nearest level i Landmark

The Landmark Hierarchy The Landmark Hierarchy doesndoesn’t’t perform well for perform well for networks with very small networks with very small diameters compared to the diameters compared to the number of routers.number of routers.

2929

SummarySummary The Landmark hierarchy has been The Landmark hierarchy has been

described.described. The Landmark hierarchy is easier to The Landmark hierarchy is easier to

dynamically configure.dynamically configure. Dynamic routing in the Landmark Dynamic routing in the Landmark

hierarchy is briefly mentioned.hierarchy is briefly mentioned.

3030

ConclusionConclusion The Landmark Hierarchy is a The Landmark Hierarchy is a

promising alternative routing promising alternative routing hierarchy, especially for large hierarchy, especially for large networks with rapidly changing networks with rapidly changing topologies.topologies.

3131

Thanks For Thanks For your attentionyour attention