Every k-edge-connected graph has a polynomially constructible spanning tree that is O(1/k)-thin for all η-near-minimum cuts with η = 1/40.
Improved approximation algorithms by generalizing the primal-dual method beyond uncrossable functions
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O(log k)-approx for Cap-k-ECSS and constant 7-approx for (1,q)-FGC via knapsack-cover inequalities plus small-cuts covering.
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Thin Trees for Near Minimum Cuts
Every k-edge-connected graph has a polynomially constructible spanning tree that is O(1/k)-thin for all η-near-minimum cuts with η = 1/40.
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Improved Approximation Algorithms for Capacitated Network Design and Flexible Graph Connectivity
O(log k)-approx for Cap-k-ECSS and constant 7-approx for (1,q)-FGC via knapsack-cover inequalities plus small-cuts covering.