![](bg2.png)
many vertices, these adaptive diagnosis techniques
require significant overhead, that is complex
analysis of the test results.
In this paper, we consider a classical system-
level diagnosis algorithm in which only the nodes
fail because a faulty communication link can be
accommodated by treating as a faulty node. And we
present a hierarchical non-adaptive diagnosis
algorithm for testing total
N nodes of computer
networks. Since general computer networks can be
regarded as an
N -nodes complete graph, then for
the efficient testing, it is essential that the test
process be parallelized to enable simultaneous test of
multiple nodes. In order to attain this object, we
propose a regular graph of connectivity-
()
1
t with
N nodes as test graphs. In this test graph, a self-
tested node is placed at a key location in a
hierarchical structure, and at first the node tests the
adjacent nodes. Only adjacent nodes that passed the
test can become new monitors and test their adjacent
nodes, and so on. This process is propagated to
higher levels of the test graph. At each level, all
monitors send the announcements of their own test
results “ I passed the test ” when they received a
qualification as a monitor first, and in addition send
only the test failed results of their test targets when
they finish their tests, back to their monitors by
which they are tested first. Each monitor also sends
data transferred from its test target back to the
monitor by which he is tested first. Then all test
results are gathered in a host ( that is , a central
observer ) directly connected the original monitor,
and then the host can locate all faults in the network.
Optimal diagnosability
is analyzed under
clustered fault distribution.
Recently, several diagnosis techniques based
on this self-testing (F.J.Meyer et al., 1989) have
proposed, and achieved a successful diagnosis of a
large number of faults. Though most of drawbacks
of self-testing are to require many self-testing,
papers (L.Zakrevski et al., 1998), and
(H.Masuyama et al., 2001) made the drawbacks
light by preparing the limited number of monitors, as
shown in our approach. However, their target
networks are multi-processor networks consisting of
homogeneous nodes connected by bi-directional
links. Each node can be viewed as a combination of
a router and processor along with associated RAM,
bus and I/O circuitry, then they differ from us in
target networks.
In non-adaptive or even adaptive tests, since each
node must performs a certain number of nodes and
report to somewhere in the network, then a traffic
problem must be cleared. Therefore, not only the
time elapsed for testing all nodes and the time
complexity of diagnosis algorithm but also the
traffic condition are essential to evaluate diagnosis
algorithms. In this paper, diagnosis latency, that is,
the time elapsed for testing all nodes is evaluated as
the total number of test times where each test
executes in different time. This time is also called as
testing round. In order to reduce the amount of
required test times, two revised approaches are
discussed and evaluated.
2 ALGORITHMS
In this section, we will discuss three algorithms for
constructing our test graph, for obtaining necessary
test orders, and for test.
2.1 Test graph
For given N and diagnosability t , we will plan to
construct a test graph whose connectivity is over
t
by the following algorithm:
[Algorithm A]
Step 1: Prepare
hypercubes of dimension
independently, and number to
these
hypercubes. Each node in a
hypercube corresponds to
)
1
nodes in each different hypercubes.
Step 2: For total
sets of
corresponding nodes, connect
corresponding nodes with a
completed graph.
Step 3: Select one node as an original monitor
arbitrary from
N nodes. Set the
edges connected with the original
monitor and the adjacent nodes as
unidirectional edges and all other
edges as bidirectional edges.
The graph obtained by Algorithm A has
β
α
2⋅ nodes, and the degree of each node is
+
)
1
. Then,
and
are restricted by
given
N and
as follows:
β
α
2⋅=N and
)
2
t . The longest distance
m
d from an
original monitor is
1
.
On the strength of algorithm A for
constructing test graph, we can give test orders to
every adjacent nodes of each node by the following
algorithm:
[Algorithm B]
Each node of a
-dimensional hypercube
can be indexed 0 to
1
2
−
β
, and each of
hypercubes can be numbered 0 to
1−
. Assume
node
i is indexed
j
and hypercube which
contain node
i is numbered
()
10 −≤≤
kk . The
test orders of each adjacent node of node
i are as
follows: The adjacent nodes indexed
)
,1
j
)
)
)
1,2,,2
jjj L
β
2.mod
on hypercube
numbered
k , the adjacent nodes on hypercubes
numbered
)
)
)( )
1,2,,2,1 −−
kkkk L
()
.mod .
ICETE 2004 - SECURITY AND RELIABILITY IN INFORMATION SYSTEMS AND NETWORKS
162