This repository contains results on popular Steiner tree instances in a simple machine- and human-readable CSV format.

The headers of our CSV files are:

1. group: the group the instance is part of (or - if there is no group)
2. filename: the file name
3. n: the number of nodes
4. m: the number of edges
5. t: the number of terminals
6. opt: the optimum solution value if known
7. lower: the best known lower bound for the optimum solution value
8. upper: the best known upper bound for the optimum solution value

Below you can find more information on the instance sets and where the bounds come from.

If no information on bounds is given, we default to self-computed values, usually a lower bound of 0 and an upper bound obtained by a run of a 2- and/or 11/6-approximation algorithm [TM80,Z93]. If the optimum solution is given, it is either computed using a standard ILP approach or by even simpler means (e.g., solved by preprocessing).

This file contains results for SteinLib instances [KMV00].

The instances are available at http://steinlib.zib.de/download.php

The bounds are taken from [DIMACS,RPRUW04,FLLLMRSS14,PV14,R15,GKMRS16,PUW18,SRK19,RSK19].

This file contains results for Vienna instances [DIMACS], see also http://homepage.univie.ac.at/ivana.ljubic/research/STP/

The instances are available at https://dimacs11.zib.de/downloads.html#stpg

All optimal solutions are taken from [PV14].

This file contains results for Copenhagen14 instances [DIMACS].

The instances are available at https://dimacs11.zib.de/downloads.html#stpg

All optimal solutions are taken from [PV14].

This file contains results for PUCN instances [DIMACS].

The instances are available at https://dimacs11.zib.de/downloads.html#stpg

The bounds are taken from [FLLLMRSS14].

This file contains results for GAPS instances [DIMACS].

The instances are available at https://dimacs11.zib.de/downloads.html#stpg

The optimal values can be computed from the given parameters. "Goemans" instances G[k1,k2] have optimal solution k2 + (k1 + 1)(k1 + 2) + 2 [PV09]. "Skutella" instances S[k] have optimal solution (3 * 7^k - 1)/2 [BGRS13].

This file contains results for EFST instances [DIMACS].

The instances are available at https://dimacs11.zib.de/downloads.html#stpg

The bounds are the best known bounds as of March 24, 2015 [DIMACS].

This file contains results for EFSTINT instances [DIMACS] (instances as of 2015-05-10).

The instances are available at https://dimacs11.zib.de/downloads.html#stpg

This file contains results for the instances used in [OS14,OS15].

The instances are available at https://sites.google.com/site/reiracofage/research

You have improved a bound? Use the GitHub features (issue a bug, fork, etc.) or contact me via e-mail: [email protected]

The files are public domain.

[BGRS13] Jarosław Byrka, Fabrizio Grandoni, Thomas Rothvoß, Laura Sanità: Steiner Tree Approximation via Iterative Randomized Rounding. Journal of the ACM 60(1), art. 6, 2013.

[DIMACS] Best bounds as of September 12, 2014 for SteinLib instances. DIMACS, 2014.

[FLLLMRSS14] Matteo Fischetti, Markus Leitner, Ivana Ljubić, Martin Luipersbeck, Michele Monaci, Max Resch, Domenico Salvagnin, Markus Sinnl: Thinning out Steiner trees: a node-based model for uniform edge costs. DIMACS, 2014.

[GKMRS16] Gerald Gamrath, Thorsten Koch, Stephen J. Maher, Daniel Rehfeldt, Yuji Shinano: SCIP-Jack – A solver for STP and variants with parallelization extensions. ZIB-Report 16-41, 2016.

[KMV00] Thorsten Koch, Alexander Martin, Stefan Voß: SteinLib: An Updated Library on Steiner Tree Problems in Graphs. ZIB-Report 00-37, 2000. See also http://steinlib.zib.de

[OS14] Ricardo Tavares de Oliveira, Fabiano Silva: SAT and MaxSAT Encodings for Trees Applied to the Steiner Tree Problem. Brazilian Conference on Intelligent Systems (BRACIS 2014): 192–197, 2014.

[OS15] Ricardo Tavares de Oliveira, Fabiano Silva: On a Relative MaxSAT Encoding for the Steiner Tree Problem in Graphs. Mexican International Conference on Artificial Intelligence (MICAI 2015): 422–434, 2015.

[PUW18] Thomas Pajor, Eduardo Uchoa, Renato F. Werneck: A Robust and Scalable Algorithm for the Steiner Problem in Graphs. Math. Program. Comput. 10(1): 69–118, 2018.

[PV09] Tobias Polzin, Siavash Vahdati Daneshmand: Approaches to the Steiner Problem in Networks. Algorithmics of Large and Complex Networks 2009: 81–103, 2009.

[PV14] Tobias Polzin, Siavash Vahdati Daneshmand: The Steiner Tree Challenge: An updated Study. DIMACS, 2014.

[R15] Daniel Rehfeldt: A Generic Approach to Solving the Steiner Tree Problem and Variants. Master Thesis, TU Berlin, 2015.

[RPRUW04] Isabel Rosseti, Marcus Poggi de Aragão, Celso C. Ribeiro, Eduardo Uchoa, Renato F. Werneck: New Benchmark Instances for the Steiner Problem in Graphs. Metaheuristics: Computer Decision-Making, 601–614, 2004.

[RSK19] Daniel Rehfeldt, Yuji Shinano, Thorsten Koch: SCIP-Jack: An exact high performance solver for Steiner tree problems in graphs and related problems. Proceedings of the 7th International Conference on High Performance Scientific Computing (HPSC 2018); Modeling, Simulation and Optimization of Complex Processes.

[SRK19] Yuji Shinano, Daniel Rehfeldt, Thorsten Koch: Building Optimal Steiner Trees on Supercomputers by Using up to 43,000 Cores. Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2019): 529–539, 2019.

[TM80] Hiromitsu Takahashi, Akira Matsuyama: An approximate solution for the Steiner problem in graphs. Math. Japonica 24(6), 573–577, 1980.

[Z93] Alexander Zelikovsky: A faster approximation algorithm for the steiner tree problem in graphs. Information Processing Letters 46(2), 79–83, 1993.