2 research outputs found
Polynomial-time Approximation Algorithm for finding Highly Comfortable Team in any given Social Network
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.Comment: The manuscript contains 38 pages and 9 Figure
Existence of Comfortable Team in some Special Social Networks
Comfortability is one of the important attributes (characteristics) for a
successful team work in any organization. It is necessary to find a comfortable
and successful team in any given social network. We have introduced
"comfortability" as a new SNA index. Comfortable team exists only in some
social networks. In this paper, we analyze the existence of comfortable team in
product graphs, such as strong product and Lexicographic product of two given
graphs.Comment: 10 pages and 6 figures. arXiv admin note: substantial text overlap
with arXiv:1406.1012, arXiv:1405.453