Models and branch-and-cut algorithms for the Steiner tree problem with revenues, budget and hop constraints

Networks ◽  
2008 ◽  
Vol 53 (2) ◽  
pp. 141-159 ◽  
Author(s):  
Alysson M. Costa ◽  
Jean-François Cordeau ◽  
Gilbert Laporte
Keyword(s):  
Steiner Tree ◽  
Branch And Cut ◽  
Steiner Tree Problem ◽  
Hop Constraints

Solving the Steiner Tree Problem on a Graph Using Branch and Cut

1992 ◽  
Vol 4 (3) ◽  
pp. 320-335 ◽  
Author(s):  
Sunil Chopra ◽  
Edgar R. Gorres ◽  
M. R. Rao
Keyword(s):  
Steiner Tree ◽  
Branch And Cut ◽  
Steiner Tree Problem

A branch-and-cut algorithm for the Steiner tree problem with delays

2011 ◽  
Vol 6 (8) ◽  
pp. 1753-1771
Author(s):  
V. Leggieri ◽  
M. Haouari ◽  
C. Triki
Keyword(s):  
Steiner Tree ◽  
Branch And Cut ◽  
Steiner Tree Problem

scholarly journals Implications, conflicts, and reductions for Steiner trees

2021 ◽  
Author(s):  
Daniel Rehfeldt ◽  
Thorsten Koch
Keyword(s):  
Steiner Tree ◽  
State Of The Art ◽  
The State ◽  
Branch And Cut ◽  
Steiner Tree Problem ◽  
New Methods ◽  
Current State ◽  
Benchmark Instances ◽  
Extensive Collection ◽  
First Time

AbstractThe Steiner tree problem in graphs (SPG) is one of the most studied problems in combinatorial optimization. In the past 10 years, there have been significant advances concerning approximation and complexity of the SPG. However, the state of the art in (practical) exact solution of the SPG has remained largely unchallenged for almost 20 years. While the DIMACS Challenge 2014 and the PACE Challenge 2018 brought renewed interest into Steiner tree problems, even the best new SPG solvers cannot match the state of the art on the vast majority of benchmark instances. The following article seeks to advance exact SPG solution once again. The article is based on a combination of three concepts: Implications, conflicts, and reductions. As a result, various new SPG techniques are conceived. Notably, several of the resulting techniques are (provably) stronger than well-known methods from the literature that are used in exact SPG algorithms. Finally, by integrating the new methods into a branch-and-cut framework, we obtain an exact SPG solver that is not only competitive with, but even outperforms the current state of the art on an extensive collection of benchmark sets. Furthermore, we can solve several instances for the first time to optimality.

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