A Representation Theorem for Union-Difference Families and Application
نویسندگان
چکیده
We give a quadratic O(|X|) space representation based on a canonical tree for any subset family F ⊆ 2 holding the closure under union and difference of overlapping members. The cardinal of F is potentially in O(2), and its size higher. As far as we know this is the first representation theorem for such families. As an application of this framework we obtain a uniqueness decomposition theorem on a digraph decomposition that captures and is strictly more powerful than the well-studied modular decomposition. Moreover a polynomial time decomposition algorithm for this case is described.
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