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Listing Small Minimal Separators of a Graph
Let be a graph and vertices of . A minimal -separator of
is an inclusion-wise minimal vertex set of that separates and .
We consider the problem of enumerating the minimal -separators of that
contain at most vertices, given some integer . We give an algorithm
which enumerates such minimal separators, outputting the first minimal
separators in at most time for all .
Therefore, our algorithm can be classified as fixed-parameter-delay and
incremental-polynomial time. To the best of our knowledge, no algorithms with
non-trivial time complexity have been published for this problem before. We
also discuss barriers for obtaining a polynomial-delay algorithm.Comment: 9 page