Steiner Tree 1.39-Approximation in Practice

Solving Steiner trees: Recent advances, challenges, and perspectives

“…However, Warme [234] showed that if the size of the maximum FSC is bounded by a constant, then the LP‐relaxation of HYP can be obtained in polynomial time. This fact has been extensively exploited in a series of articles that provide LP‐based approximation algorithms for the STP [23, 25, 37, 110, 147] (cf. Section 9).…”

“…Approximation algorithms based on hypergraphic LP‐relaxations have been implemented and empirically tested by Beyer et al [23, 25]; see also Section 9. However, to the best of our knowledge, there are no empirical studies on exact methods for the STP in graphs derived from HYP.…”

“…They also showed that the exact method by Polzin and Vahdati Daneshmand [183] was faster and applicable to larger graphs than the combinatorial approximation algorithms. In a subsequent study, Beyer and Chimani [23] implemented the (1.39 + ϵ )‐approximation algorithm following the recipe of Goemans et al [110]. They concluded that a practical implementation can be achieved for k = 3; however the algorithm was still not competitive against the TM heuristic or a simple B&C derived from the DCUT formulation (see also Ciebiera et al [56] for similar conclusions).…”