Extending Reduction Techniques for the Steiner Tree Problem

Reduction tests for the prize-collecting Steiner problem

“…The sequence of results reported in [13,15,16,19,17,14,12] on the main benchmark instances from the literature [8] improve by two or three orders of magnitude upon the results from previous articles, like [7]. The strength of those new algorithms lies on a complex combination of reduction tests, primal heuristics, dual heuristics and branch-and-cut.…”

“…More recently, Uchoa et al [17] enhanced Duin and Volgenant's tests with the idea of expansion. This idea was further developed by Polzin and Vahdati [14]. The reduction tests with expansion still rely on Bottleneck Steiner distances.…”

Optimal Interconnection Trees in the Plane

“…Duin [141] and Uchoa, Aragão and Ribeiro [373] extended the ideas of Winter further, resulting in powerful reductions for grid graphs coming from chip design. Currently, the fastest and most powerful graph reduction techniques are due to Polzin and Vahdati Daneshmand [306,308,309,375].…”

Algorithm Engineering – An Attempt at a Definition

“…In particular for the first three problems the benchmarks have helped enable astonishing breakthroughs. Using deep mathematical insights into the structure of the problems one can now compute optimal solutions even for large, realistic instances of the travelling salesman problem [53] and of the Steiner tree problem [54]. It is a bit odd that similar benchmarks for problems that are polynomially solvable are sometimes more difficult to obtain.…”