Enumerating Minimal Separators in Ranked Order

11/15/2021

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by   Batya Kenig, et al.

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Let G be an n-vertex graph, and s,t vertices of G. We present an efficient algorithm which enumerates the set of minimal st-separators of G in ascending order of cardinality, with a delay of O(n^3.5) per separator. In particular, we present an algorithm that lists, in ascending order of cardinality, all minimal separators with at most k vertices. In that case, we show that the delay of the enumeration algorithm is O(kn^2.5) per separator. Our process is based on a new method that can decide, in polynomial time, whether the set of minimal separators under certain inclusion, exclusion, and cardinality constraints is empty.