On the Exact Solution of Prize-Collecting Steiner Tree Problems

The prize– collecting Steiner tree problem (PCSTP) is a well– known generality of the classic Steiner tree problem in graphs, with a large number of practical plays. It attracted particular interest during the 11th DIMACS Challenge in 2014, and since either, several PCSTP solvers have been introduced in the literature. Although these new solvers further, and hourly drastically, helped on the results of the DIMACS Challengemultiple PCSTP measure illustrations have remained unsolved. The following paper describes farther advances in the state of the art in exact PCSTP unraveling. It introduces new recipes and algorithms for PCSTP, involving polychromatic new metamorphoses (or reductions) of PCSTP illustrations to improvised problems, for instance, to drop the problem size or to get a better integer programming utterance. Several of the new recipes and algorithms provably dominate former approachesFarther theoretical plats of the new factorsditto as their complexity, are battedAlsonew complexity results for the exact result of PCSTP and allied problems are described, which form the base of the algorithm designUltimately, the new developments also restate into a strong computational performance the reacting exact PCSTP solver outperforms all former approaches, both in terms of runtime and solvability. In particular, it solves several formerly intractable measure illustrations from the 11th DIMACS Challenge to optimality. Either, several new introduced large-scale illustrations with up to 10 million edgesanteriorly considered to be too large for any exact approach, can now be doped to optimality in subordinate than two hours.

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