The paper presents a polynomial-time algorithm for the k-Edge-Connected Spanning Subgraph (k-ECSS) problem that returns a solution of cost no greater than the cheapest (k+10)-ECSS on the same graph.
The key highlights are:
The algorithm uses a new technique called "ghost value augmentation" to enhance the iterative relaxation framework and achieve high sparsity in intermediate problems.
The algorithm's guarantees improve upon the best-known 2-approximation for k-ECSS whenever the optimal value of (k+10)-ECSS is close to that of k-ECSS. This property holds for the closely related k-Edge-Connected Spanning Multi-Subgraph (k-ECSM) problem.
As a consequence, the algorithm achieves a (1+O(1/k))-approximation for k-ECSM, resolving a conjecture of Pritchard and improving upon a recent (1+O(1/√k))-approximation.
The paper also presents a matching lower bound for k-ECSM, showing the approximation ratio is tight up to the constant factor in O(1/k), unless P=NP.
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by D Ellis Hers... في arxiv.org 04-08-2024
https://arxiv.org/pdf/2311.09941.pdfاستفسارات أعمق