Disjoint Paths Multi-stage Interconnection Networks Stability Problem
This research paper emphasizes that the Stable Matching
problems are the same as the problems of stable configurations of
Multi-stage Interconnection Networks (MIN). The authors have
solved the Stability Problem of Existing Regular Gamma Multistage
Interconnection Network (GMIN), 3-Disjoint Gamma
Multi-stage Interconnection Network (3DGMIN) and 3-Disjoint
Path Cyclic Gamma Multi-stage Interconnection Network
(3DCGMIN) using the approaches and solutions provided by the
Stable Matching Problem. Specifically Stable Marriage Problem
is used as an example of Stable Matching. For MINs to prove
Stable two existing algorithms are used:-the first algorithm
generates the MINs Preferences List in O(n2 ) time and second
algorithm produces a set of most Optimal Pairs of the Switching
Elements (SEs) (derived from the MINs Preferences List) in
O(n) time. Moreover, the paper also solves the problem of Ties
that occurs between the Optimal Pairs. The results are promising
as the comparison of the MINs based on their stability shows that
the ASEN, ABN, CLN, GMIN, 3DCGMIN are highly stable in
comparison to HZTN, QTN, DGMIN. However, on comparing
the irregular and regular MINs in totality upon their stability the
regular MINs comes out to be more stable than the irregular
MINs.
Keywords: Disjoint Paths, Networks, Stability Problem
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