Resource allocation problems: algorithmic approaches
Resource allocation problems: algorithmic approaches
Augmenting graphs to meet edge-connectivity requirements
SIAM Journal on Discrete Mathematics
Applications of submodular functions
Surveys in combinatorics, 1993
A note on minimizing submodular functions
Information Processing Letters
Simultaneous Augmentation of Two Graphs to an l-Edge-Connected Graph and a Biconnected Graph
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
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Let V be a finite set, and R be the set of reals. We consider the polyhedron P = {z ∈ R-V | Σi∈X z(i) ≤ f(X), ¬X ∈ 2V} for a system (V, f) with an intersecting submodular and posi-modular set function f : 2V → R, where R-V denotes the set of |V|-dimensional nonpositive vectors. We first prove that there is a laminar family χ ⊆ 2V such that P is characterized by {z ∈ R-V| Σi∈X z(i) ≤ f(X), ¬X ∈ χ}. Based on this, we can solve in polynomial time the edge-connectivity augmentation problem with an additional constraint that the number of vertices to which new edges are incident is minimized.