05 1 mobile_computing

Mobile and Wireless Computing
Institute for Computer Science, University of Freiburg
Western Australian Interactive Virtual Environments Centre (IVEC)
Lecture 5 : Link Reversal Routing
Lecture 5.1 : Basic ideas behind Link Reversal
Routing
Lecture 5.2 : The Gafni-Bertsekas algorithm for
Link Reversal Routing

Link Reversal Routing (LRR)
Link Reversal Routing is suitable for ad hoc
mobile networks that do not fall under the
following two categories :
– The rate of topological changes are not so fast as to
make flooding the only possible routing method.
– Also, the changes are not so slow that it is possible to
maintain shortest paths efficiently.
However, the success of the LRR method
depends on other factors like network size,
network topology and available bandwidth.

General Approach
The main objective of the LRR approach is to
reduce the number of control messages due to
topological changes.
The LRR approaches do not try to maintain
extensive routing tables like proactive protocols.
Instead, the main aim of all LRR approaches is
to maintain a directed acyclic graph (DAG)
rooted at the destination.

Directed Acyclic Graph
The destination is the only node that may have
only incoming links. All other nodes that have
incoming links must also have outgoing links.
We will talk about only a single destination and
the DAG associated with it.
However, it should be noted that at any time all
the nodes in the network may be destinations of
messages from other nodes.

Directed Acyclic Graph
Each such destination will have a rooted DAG
associated with it.
If we consider a single destination D, a rooted
DAG provides multiple paths to D.
However, if we consider another node N, there
is no knowledge in N that can be used by N to
decide its position in the DAG relative to D.

An Example
Dest
Each node only knows its one-hop neighbours and
does not get any information from other nodes.

An Example
Dest
This DAG is drawn assuming only one destination.
In general there may be many destinations and each
node except the destination will try to maintain at least
one outgoing link to participate in the DAG.

An Example
Dest
Since the overall DAG has no cycles, no message will
loop around a cycle and each message will eventually
reach its destination.

Difference from Other Protocols
Unlike table-driven protocols like DSDV, the
LRR approaches do not require global
information.
Unlike reactive protocols like DSR and AODV,
there is no need to find a path to a destination
through route request messages.
LRR approaches have lower overheads in terms
of control packets as well as lower latency in
finding paths.

Maintaining the DAG
One of the key issues in all LRR based protocols
is to maintain the DAG correctly. This is done
differently in different protocols.
We will first discuss the situation when a node
needs to take some action for maintaining the
overall DAG.
We will discuss the maintenance procedure for
different protocols later.

What Triggers Route or DAG Maintenance
i j
k
For a node i, if there is a directed edge from i to
j, then i is called the upstream neighbour of j and
j is called the downstream neighbour of i.
A node needs to initiate route maintenance if it
has lost all of its downstream neighbours.

Triggering DAG Maintenance
i
upstream
downstream
DAG maintenance only affects those nodes for whom all
previous directed paths pass through node i.
Hence, DAG maintenance has mostly local effects in
LRR protocols.

The General Scenario for Multiple Destinations
d1
d2
d3
d4
i j
For two neighbours i and j, i can be both upstream and
downstream neighbour of j depending on the destination.
For destinations d1, d2 and d4, i is the upstream
neighbour of j. For d3, i is the downstream neighbour of j.
The status of each link is stored in each node tagged with
the destination ID.

Gafni-Bertsekas (GF) Algorithm
The GF algorithm was first proposed for routing
in packet radio networks. The aim was to solve
the following problem :
– Given a connected, destination-disoriented DAG,
transform it into a destination-oriented DAG by
reversing the directions of some of its links.
We consider only one destination node, however
the algorithm can be executed concurrently for
multiple destination nodes.

Some Definitions
A DAG is destination-oriented, if for every node
n there exists a directed path originating at n
and terminating at the destination.
Otherwise, the DAG is destination-disoriented.
The whole idea behind the GF algorithm is :
Given a destination, change the directions of
some of the links in the DAG so that it becomes
destination-oriented.

A Destination-Oriented DAG
Dest
We can make the DAG destination-disoriented if we
change it so that there is at least one node (other than
the destination) with no outgoing edges.

A Simple Theorem
Theorem : A DAG is destination-disoriented if
and only if there exists a node other than the
destination that has no outgoing link.
Proof : if :
Suppose there is a node n (other than the
destination) which has no outgoing link. Clearly,
n does not have a path to the destination since it
has no outgoing links.

A Simple Theorem
Only if : Suppose there is at least one node n
such that n does not have a path to the
destination.
Since our network is a DAG, it is not possible
that a path from n will loop around a cycle.
Hence paths from n will fail to reach the
destination only if they reach a node without any
outgoing link.

Destination-Oriented DAG
Hence, to maintain a destination-oriented DAG,
we have to ensure the following :
– Every node except the destination has at least one
outgoing edge. This is ensured by reversing link
directions in the DAG.
– The underlying network should remain a DAG when
we perform link reversals.

Full Reversal and Partial Reversal Methods
The GF algorithm provides two methods for link
reversal : full reversal and partial reversal.
Full Reversal : If a node n (other than the
destination) has no outgoing links, it reverses
the directions of all of its incoming links.
Full reversals propagate through the network
until each node (except the destination) has at
least one outgoing link.

Full Reversal Example
1
2 3
4 5 6
dest

1
2 3
4 5 6
dest
Link failure
Nodes that reverse

Nodes that reverse
1
2 3
4 5 6
dest
Link failure

Nodes that reverse
1
2 3
4 6
dest
Link failure
5

Full Reversal is Loop Free
Assume that a loop is formed when a node n
does a full reversal.
In that case, one of the nodes on the loop must
be n.
However, n has only outgoing links after the full
reversal. Hence, n cannot be part of a loop.

Full Reversal Does not Oscillate
The GF algorithm assumes that the network is
always connected.
Hence, there is at least one node P with an
outgoing link to the destination.
P will never execute a full reversal and hence
the iteration will stop at P.
However, GF algorithm does not work if the
network is partitioned. A partitioned network may
result in infinite oscillation of full reversal.

GF Fails to Converge for Partitioned Networks
dest
1
2
3 4
5
Link failure
Nodes that reverse

dest
1
2
3 4
5
Nodes that reverse

2
dest
1
3 4
5
Nodes that reverse

05 1 mobile_computing

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