190 research outputs found
Hybrid Fault diagnosis capability analysis of Hypercubes under the PMC model and MM* model
System level diagnosis is an important approach for the fault diagnosis of
multiprocessor systems. In system level diagnosis, diagnosability is an
important measure of the diagnosis capability of interconnection networks. But
as a measure, diagnosability can not reflect the diagnosis capability of
multiprocessor systems to link faults which may occur in real circumstances. In
this paper, we propose the definition of -edge tolerable diagnosability to
better measure the diagnosis capability of interconnection networks under
hybrid fault circumstances. The -edge tolerable diagnosability of a
multiprocessor system is the maximum number of faulty nodes that the system
can guarantee to locate when the number of faulty edges does not exceed
,denoted by . The PMC model and MM model are the two most widely
studied diagnosis models for the system level diagnosis of multiprocessor
systems. The hypercubes are the most well-known interconnection networks. In
this paper, the -edge tolerable diagnosability of -dimensional hypercube
under the PMC model and MM is determined as follows: ,
where , .Comment: 5 pages, 1 figur
Conditional Fault Diagnosis of Bubble Sort Graphs under the PMC Model
As the size of a multiprocessor system increases, processor failure is
inevitable, and fault identification in such a system is crucial for reliable
computing. The fault diagnosis is the process of identifying faulty processors
in a multiprocessor system through testing. For the practical fault diagnosis
systems, the probability that all neighboring processors of a processor are
faulty simultaneously is very small, and the conditional diagnosability, which
is a new metric for evaluating fault tolerance of such systems, assumes that
every faulty set does not contain all neighbors of any processor in the
systems. This paper shows that the conditional diagnosability of bubble sort
graphs under the PMC model is for , which is about four
times its ordinary diagnosability under the PMC model
The -good neighbor conditional diagnosability of locally exchanged twisted cubes
Connectivity and diagnosability are important parameters in measuring the
fault tolerance and reliability of interconnection networks. The
-vertex-connectivity of a connected graph is the minimum cardinality
of a faulty set such that is disconnected and every
fault-free vertex has at least fault-free neighbors. The -good-neighbor
conditional diagnosability is defined as the maximum cardinality of a
-good-neighbor conditional faulty set that the system can guarantee to
identify. The interconnection network considered here is the locally exchanged
twisted cube . For and , we first
determine the -vertex-connectivity of , then establish the
-good neighbor conditional diagnosability of under the PMC model
and MM model, respectively.Comment: 19 pages, 4 figure
The -good neighbour diagnosability of hierarchical cubic networks
Let be a connected graph, a subset is called an
-vertex-cut of if is disconnected and any vertex in has
at least neighbours in . The -vertex-connectivity is the size
of the minimum -vertex-cut and denoted by . Many
large-scale multiprocessor or multi-computer systems take interconnection
networks as underlying topologies. Fault diagnosis is especially important to
identify fault tolerability of such systems. The -good-neighbor
diagnosability such that every fault-free node has at least fault-free
neighbors is a novel measure of diagnosability. In this paper, we show that the
-good-neighbor diagnosability of the hierarchical cubic networks
under the PMC model for and the model for is , respectively
Relationship between Conditional Diagnosability and 2-extra Connectivity of Symmetric Graphs
The conditional diagnosability and the 2-extra connectivity are two important
parameters to measure ability of diagnosing faulty processors and
fault-tolerance in a multiprocessor system. The conditional diagnosability
of is the maximum number for which is conditionally
-diagnosable under the comparison model, while the 2-extra connectivity
of a graph is the minimum number for which there is a
vertex-cut with such that every component of has at least
vertices. A quite natural problem is what is the relationship between the
maximum and the minimum problem? This paper partially answer this problem by
proving for a regular graph with some acceptable
conditions. As applications, the conditional diagnosability and the 2-extra
connectivity are determined for some well-known classes of vertex-transitive
graphs, including, star graphs, -star graphs, alternating group
networks, -arrangement graphs, alternating group graphs, Cayley graphs
obtained from transposition generating trees, bubble-sort graphs, -ary
-cube networks and dual-cubes. Furthermore, many known results about these
networks are obtained directly
The tightly super 3-extra connectivity and 3-extra diagnosability of crossed cubes
Many multiprocessor systems have interconnection networks as underlying
topologies and an interconnection network is usually represented by a graph
where nodes represent processors and links represent communication links
between processors. In 2016, Zhang et al. proposed the -extra diagnosability
of , which restrains that every component of has at least
vertices. As an important variant of the hypercube, the -dimensional crossed
cube has many good properties. In this paper, we prove that
is tightly super 3-extra connected for and the 3-extra
diagnosability of is under the PMC model and MM
model
On the -good-neighbor connectivity of graphs
Connectivity and diagnosability are two important parameters for the fault
tolerant of an interconnection network . In 1996, F\`{a}brega and Fiol
proposed the -good-neighbor connectivity of . In this paper, we show that
for , and graphs with and
trees with for are
characterized, respectively. In the end, we get the three extremal results for
the -good-neighbor connectivity.Comment: 14 pages, 2 figures. arXiv admin note: substantial text overlap with
arXiv:1904.06527; text overlap with arXiv:1609.08885, arXiv:1612.05381 by
other author
Cycles in enhanced hypercubes
The enhanced hypercube is a variant of the hypercube . We
investigate all the lengths of cycles that an edge of the enhanced hypercube
lies on. It is proved that every edge of lies on a cycle of every
even length from to ; if is even, every edge of also
lies on a cycle of every odd length from to , and some special
edges lie on a shortest odd cycle of length .Comment: 9 pages, 2 figure
The Component Connectivity of Alternating Group Graphs and Split-Stars
For an integer , the -component connectivity of a
graph , denoted by , is the minimum number of vertices
whose removal from results in a disconnected graph with at least
components or a graph with fewer than vertices. This is a natural
generalization of the classical connectivity of graphs defined in term of the
minimum vertex-cut and is a good measure of robustness for the graph
corresponding to a network. So far, the exact values of -connectivity are
known only for a few classes of networks and small 's. It has been
pointed out in~[Component connectivity of the hypercubes, Int. J. Comput. Math.
89 (2012) 137--145] that determining -connectivity is still unsolved for
most interconnection networks, such as alternating group graphs and star
graphs. In this paper, by exploring the combinatorial properties and
fault-tolerance of the alternating group graphs and a variation of the
star graphs called split-stars , we study their -component
connectivities. We obtain the following results: (i) and
for , and for
; (ii) , , and
for
The vulnerability of the diameter of enhanced hypercubes
For an interconnection network , the {\it -wide diameter}
is the least such that any two vertices are joined by
internally-disjoint paths of length at most , and the {\it
-fault diameter} is the maximum diameter of a
subgraph obtained by deleting fewer than vertices of .
The enhanced hypercube is a variant of the well-known hypercube.
Yang, Chang, Pai, and Chan gave an upper bound for and
and posed the problem of finding the wide diameters and
fault diameters of . By constructing internally disjoint paths between
any two vertices in the enhanced hypercube, for and we
prove
where is the diameter of . These results mean that
interconnection networks modelled by enhanced hypercubes are extremely robust.Comment: 9 pages, 1 figur
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