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In an instance of the (directed) Max Leaf Tree (MLT) problem we are given a vertex-weighted (di)graph G(V,E,w) and the goal is to compute a subtree with maximum weight on the leaves. The weighted Connected Max Cut (CMC) problem takes in an undirected edge-weighted graph G(V,E,w) and seeks a subset S⊆V such that the induced graph G[S] is connected and ∑e∈δ(S)w(e) is maximized.We obtain a constant approximation...
Given an n-vertex digraph $$D = (V, A)$$ D = ( V , A ) the Max- $$k$$ k -Ordering problem is to compute a labeling $$\ell : V \rightarrow [k]$$ ℓ : V → [ k ] maximizing the number of forward edges, i.e. edges (u, v) such that $$\ell (u) < \ell (v)$$ ℓ ( u ) < ℓ ( v ) . For different values of k, this reduces to maximum acyclic subgraph ( $$k=n$$ k...
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