Efficient algorithms and methods to solve dynamic MINs stability problem using stable matching with complete ties

Abstract

We claimed that Stable Matching problems are the same as problems about stable configurations of Multi-stage Interconnection Networks (MINs). We solved the Regular and Irregular MINs Stability Problems using the approaches and solutions provided by the Stable Matching Problem. Specifically we have used Stable Marriage Problem as an example of Stable Matching. Two algorithms are proposed:-the first algorithm generates the MINs Preferences List in O(n 2 ) 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. Consequences include new algorithms for finding a Stable Matching between the SEs, an understanding of the difference between MINs Stability and Unstability problems, Algorithms used for generating the Preference Lists for the MINs, methods, and procedures used for deriving the Optimal Pairs from the MINs Preference Lists, and solving ties between them.

Comparative analysis of Traffic Patterns on k-ary n-tree using adaptive algorithms based on Burton Normal Form

“…A number of techniques have been used to increase the reliability and fault-tolerance of the INs. A survey of the fault-tolerance attributes of these networks can be found in [1][2][3][4][5][6][7].…”

“…INs are based on three aspects: Network Topology, the Routing Algorithm, and the Flow Control mechanism employed [1][2][3][4][5][6][7][8][9][10]. One of three prime aspects of INs is topology.…”

Stochastic communication for application-specific Networks-on-Chip

“…With the performance requirement of the switches/routers exceeding several terabits/sec and teraflops/sec, it becomes imperative to make them dynamic and fault-tolerant. The typical modern day application of the MINs includes fault-tolerant packet switches, designing unicast, and multicast router fabrics [22][23][24][25][26][27][28][29][30][31][32][33]. [4][5][6][7].…”

Designing a Fault-tolerant Fully-Chained Combining Switches Multi-stage Interconnection Network with Disjoint Paths

“…This one path had only one switching element in its middlemost stage and whose failure could result in a choking condition. There were also other approaches, explained in [9] as the hybrid ZETA Network, Augmented Baseline Network, Quad-tree Network, and Augmented Shuffle-Exchange Network, which uses multiplexers, demultiplexers, and chaining links in an attempt to provide fault-tolerance. However, these approaches were only fault-tolerant for some cases.…”

“…Interconnection Networks (IN) [1][2][3][4][5][6][7][8][9][10] are used to design a network in which there are several independent paths between two modules being connected which increases the available bandwidth. Many stages of inter-connected switches form a MIN.…”