Discrete OptimizationAn algorithmic framework for the exact solution of tree-star problems

- The framework considers connected facility location, (generalized) Steiner tree-star, rent-or-buy problems.
- Dual ascent algorithm for asymmetric connected facility location is an important ingredient.
- Problem reductions techniques are used.
- Many unsolved instances from literature solved to optimality within a few seconds.
- The construction heuristic of the framework also works very good on its own.

Many problems arising in the area of telecommunication ask for solutions with a tree-star topology. This paper proposes a general procedure for finding optimal solutions to a family of these problems. The family includes problems in the literature named as connected facility location, rent-or-buy and generalized Steiner tree-star. We propose a solution framework based on a branch-and-cut algorithm which also relies on sophisticated reduction and heuristic techniques. An important ingredient of this framework is a dual ascent procedure for asymmetric connected facility location. This paper shows how this procedure can be exploited in combination with various mixed integer programming formulations. Using the new framework, many benchmark instances in the literature for which only heuristic results were available so far, can be solved to provable optimality within seconds. To better assess the computational performance of the new approach, we additionally consider larger instances and provide optimal solutions for most of them too.