A Fast $f(r,k+1)/k$f(r,k+1)/k-Diagnosis for Interconnection Networks Under MM* Model

Cyberspace is not a “vacuum space”, and it is normal that there are inevitable viruses and worms in cyberspace. Cyberspace security threats stem from the problem of endogenous security, which is caused by the incompleteness of theoretical system and technology of the information field itself. Thus it is impossible and unnecessary for us to build an “aseptic” cyberspace. On the contrast, we must focus on improving the “self-immunity” of network. Literally, endogenous security is an endogenous effect from its own structural factors rather than external ones. The
$t/k$
-diagnosis strategy plays a very important role in measuring endogenous network security without prior knowledge, which can significantly enhance the self-diagnosing capability of network. As far as we know, few research involves
$t/k$
-diagnosis algorithm and
$t/k$
-diagnosability of interconnection networks under MM* model. In this article, we propose a fast
$f(r,k+1)/k$
-diagnosis algorithm of complexity
$O(Nr^2)$
, say
$G$
MIS
$k$
DIAGMM*, for a general
$r$
-regular network
$G$
under MM* model by designing a 0-comparison subgraph
$M_0(G)$
, where
$N$
is the size of
$G$
. We determine that the
$t/k$
-diagnosability
$(t(G)/k)^M$
of
$G$
under MM* model is
$f(r,k+1)$
by
$G$
MIS
$k$
DIAGMM* algorithm. Moreover, we establish the
$(t(G)/k)^M$
of some interconnection networks under MM* model, including BC networks,
$(n,l)$
-star graph networks, and data center network DCells. Finally, we compare
$(t(G)/k)^M$
with diagnosability, conditional diagnosability, pessimistic diagnosability, extra diagnosability, and good-neighbor diagnosability under MM* model. It can be seen that
$(t(G)/k)^M$
is greater than other fault diagnosabilities in most cases.