I'm leaving, and there's no new lab manager lined up. This presentation contains hopefully helpful advice on
- F\A is a matching in (V,E)
- F\E is a branching in (V,A)
- F contains no cycles in the underlying undirected graph for G
Let T be the Tutte matrix for (V,E) and let B be the branching matrix for (V,A). Tutte showed that the rank of T is twice the size of a maximum matching of (V,E), and Chaiken and Kleitman (1978) related the determinant of B to the number of branchings of (V,E). Using these results, we show that the rank of T+B is the maximum number of vertices covered by a matching forest in G.
We also present an algorithm that uses the methods of Geelen (97,98) to find an integer evaluation C of T+B, such that the rank of C is
equal to the rank of T+B.
We also propose a simple greedy algorithm, and introduce other possible
paradigms that build a tree by screening the edges provided by
Hypercleaning in the decreasing order of support from sequence data.
Extensive simulation studies are also presented to demonstrate the
efficiency and effectiveness of Hypercleaning.