A Combinatorial Model for Improved Calculation of Network Stability

چکیده مقاله

The stability and vulnerability of networks is of paramount importance in com- munications sciences and also in a variety of other fields. The theoretical basis of calculating parameters describing networks and as such optimizing networks, has proven to be valuable and has created a wealth of research in this field [1, 6, 8, 9, 10]
However, for many such parameters and studies, very high orders of com- putation are required [4, 5, 7] rendering them difficult to apply to large scale projects and thus limiting their application. Research upon novel methods and programs to study and calculate the stability of a network is therefore necessary in order to improve their efficacy and applicability.
In this article, we present our research on the stability of networks using a combinatorial approach obtaining optimization models with the ability to calculate, demonstrate and optimize the stability and vulnerability of networks. Due to the linearity of these models and the limited number of binary variables present, computation order is decreased for most cases and calculations can be completed faster which can be used for larger projects. Due to the optimization nature of this model, in addition to the calculation of parameters describing the stability of a network, it can be used to optimize the design of a network by maximizing such a parameter simultaneous to other constrictions required for any specific network design required.

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