How Many Steiner Terminals Can You Connect in 20 Years?

SCIP-Jack—a solver for STP and variants with parallelization extensions

“…Injective. S is the only solution to P that is mapped by (9) and (10) to S: EachS ∈ S , S = S contains at least one arc (v, w) such that (v, w) / ∈ A S and (w, v) / ∈ A S , since only substituting arcs in A S by there anti-parallel counterparts would not allow directed paths from the root to all vertices. Therefore,S is not mapped onto S.…”

“…In our case this occurred in two steps: First, prior to the DIMACS Challenge, with the developments delineated above, and second, after the completion of the Challenge, when further algorithmic methods were devised and implemented to considerably enhance the performance of SCIP-Jack. Further examples of revisiting research topics can be found in [10,11].…”

An approximation algorithm for the Steiner connectivity problem

“…If the number of terminal nodes is fixed, it can be solved in (pseudo‐) polynomial time by dynamic programming using a reduction to the directed Steiner tree problem, compare with . The two‐terminal case even gives rise to a TDI formulation and associated min‐max theorems . The case when all nodes are terminals can be interpreted as a submodular set covering problem .…”

“…The two‐terminal case even gives rise to a TDI formulation and associated min‐max theorems . The case when all nodes are terminals can be interpreted as a submodular set covering problem . As such, it allows a best‐possible approximation ratio of , where is the set of nodes .…”

“…As such, it allows a best‐possible approximation ratio of , where is the set of nodes . Alternative combinatorial proofs based on polymatroids and a direct Chvátal‐type argument were given in and , respectively. A polyhedral model hierarchy similar to the Steiner tree case has been derived that yields very good computational results.…”