I am working in an algorithm which finds a unique maximal independent set of vertices. Then, using this set, one can construct all other vertex subsets. I assume this might have some applications outside mathematics, especially in computer science, but I am not sure where I can read about such applications. Does anyone have any good literature suggestion which describes scenarios where this could be useful? The idea is somehow similar to that of using edge activities as defined by Tutte in order to construct all possible subgraphs of a given graph by using the set of its trees.
This does not seem likely to be useful in any application. We already know of straightforward algorithms for constructing all vertex subsets, and they are are about as efficient as possible. So, if you have a complicated way to construct all vertex subsets, that's not particularly useful, as it is a more complicated way to do something we already know how to do in a simpler way. I cannot imagine any reason why an application would choose your method instead of standard methods.