Polynomial-time Approximation Algorithm for finding Highly Comfortable Team in any given Social Network

Lakshmi Prabha S; T. N. Janakiraman

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arXiv · 1405.4534

Polynomial-time Approximation Algorithm for finding Highly Comfortable Team in any given Social Network

Lakshmi Prabha S·T. N. Janakiraman

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Abstract

There are many indexes (measures or metrics) in Social Network Analysis (SNA), like density, cohesion, etc. In this paper, we define a new SNA index called "comfortability". One among the lack of many factors, which affect the effectiveness of a group, is "comfortability". So, comfortability is one of the important attributes (characteristics) for a successful team work. It is important to find a comfortable and successful team in any given social network. In this paper, comfortable team, better comfortable team and highly comfortable team of a social network are defined based on \textbf{graph theoretic concepts} and some of their structural properties are analyzed. It is proved that forming better comfortable team or highly comfortable team in any connected network are NP-Complete using the concepts of domination in graph theory. Next, we give a polynomial-time approximation algorithm for finding such a highly comfortable team in any given network with performance ratio O(\ln \Delta), where \Delta is the maximum degree of a given network (graph). The time complexity of the algorithm is proved to be O(n^{3}), where n is the number of persons (vertices) in the network (graph). It is also proved that our algorithm has reasonably reduced the dispersion rate.

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Lakshmi Prabha S, T. N. Janakiraman. 2014-05-18. Polynomial-time Approximation Algorithm for finding Highly Comfortable Team in any given Social Network. https://arxiv.org/abs/1405.4534

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