A Graph Transformation System Model
of Reliable Dynamic Communication
Networks for Location Transparent
Mobile Agents
M. Kurihara (Hokkaido Univ., Japan)
and
M. Numazawa (Otaru Univ. Commerce, Japan)
Introduction
Distributed software technologies
Mobile agents are
software agents that
can move around the
network.
research
Mobile agent technology
practice
Future intelligent
telecommunication technologies
Introduction (2)
mobile agent network
Location transparent
Static: reliable
Dynamic: sound
Structure of this talk
1. Mobile agents
& location transparency
2. Proxy networks
(Reliablity)
3. Graph transformation system
(Soundness)
Mobile Agents

Software agents that can move around
the network
Host 1
Host 2
agent
stop
move
location transparent
network
resume
Location Transparency

The communications will not fail
even if agent B has moved to B’
without any notice to A.
communicating
A
B
move
B'
Can communicate?
In the location transparent network, yes.
Approaches to location transparency
(system-level implementation)



Logging: the agents leave (in the agent
server) the trail information containing the
next location
Brute Force: the system searches for the
target agent by sending a query to every
agent server
Registration: the system keeps the locations
of all agents in a unique directory server,
updating the information each time an agent
makes a move
Proxy Networks
(application-level implementation of
location transparency)
Basic idea: simple communication path for
forwarding messages
forward
A
forward
B
B'
B"
proxy
proxy
target
Problems
Reliability: what if a proxy is abnormal?
Performance: O(the length of the path)
Reliable and more efficient
proxy networks
Normal proxies
Special proxy
Target


Reliable: one abnormal proxy is allowed.
Performance: there is a shorter path.
Formal Representation
(graph-theoretical definition of proxy networks)
A proxy network is a finite, simple, directed acyclic graph
G=(V, E) that satisfy the following three conditions (in the
next slide).
(The vertexes of V are called agents, and the directed edges of
E are called links. By definition, a simple graph contains no
parallel edges, which connect the same start and end vertexes;
and an acyclic graph contains no circuits.)
Graph-theoretical definition of proxy networks (Contd.):
the three conditions
1. There exists a unique agent (called the target) with no
outgoing links. (The agents other than the target are called
proxies.)
2. There exists a unique proxy (called the special proxy) with
exactly one outgoing link. The link should be connected to the
target.
3. The remaining proxies (called normal proxies) have exactly
two outgoing links.
Theorem 1 (Reliability)

For all pairs of distinct proxies v and w,
there exists a path from v to the target
t without passing through w.
v
w
t
Proof of Theorem 1

Start from v and follow an appropriate
path as follows.

At normal proxies, follow a link whose
end vertex is not w.
normal proxy
w
 Repeat this process while you are at a
normal proxy.
Proof of Theorem 1 (Contd.)

Eventually, you will reach either the
special proxy or the target.

If you are at the target, you are done.

Otherwise, you are at the special proxy.
Follow the link connected to the target.
special proxy
t
Graph Transformation Rule
(V , E ) s ,t  (V  {u}, E  {( t , u ), ( s, u )})t ,u
s
t
(a) Move to a new host
s
t
u
Graph Transformation System
s
t
s
t
s
t
s
t
s
t
(a) Move to a new place
s
t
(b) Move to the special proxy
u
s
t
u
(c) Move to a normal proxy
u
v
s
t
(d) Bypass
u
v
u
The initial network G0
s
t
G0  (V0 , E0 ) s ,t
V0  {s, t}, E0  {( s, t )}
Application of graph rewrite rules
G0  G1  G2    Gn
G0  Gn
*
Theorem 2 (Soundness)
G0  G ,
then G is a proxy network.
 If
*
Summary
1. Mobile agents
& location transparency
2. Proxy networks
(Reliablity)
3. Graph transformation system
(Soundness)
Future Work

Formal theory of more complex mobile
agent systems
that might allow us (or even agents)
to rigorously (or mechanically) reason about
the dynamic nature of the networks.