Implications, Conflicts, and Reductions for Steiner Trees

Rehfeldt, Daniel; Koch, Thorsten

doi:10.1007/978-3-030-73879-2_33

Cited by 10 publications

(8 citation statements)

References 23 publications

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“…Most importantly, the latest SCIP-Jack outperforms the well-known SPG solver by Polzin and Vahdati [83,110] on almost all nontrivial benchmark testsets from the literature. See the preprint [87] for more details. Notably, Polzin and Vahdati [83,110] had remained out of reach for almost 20 years for any other SPG solver.…”

Section: Scip-sdpmentioning

confidence: 99%

“…For SPG, a central new feature is a distance concept that provably dominates the well-known bottleneck Steiner distance from Duin and Volgenant [25], see Rehfeldt and Koch [89] for details. This distance concept is used in several (new) reduction methods implemented in SCIP-Jack 2.0.…”

Section: Scip-sdpmentioning

confidence: 99%

“…Also, the new SCIP-Jack includes a full-fledged implementation of so-called extended reduction techniques. These methods are provably stronger than the state-of-the-art implementation [84], and also yield strong practical results, see Rehfeldt and Koch [87] for details. Furthermore, decomposition methods for the SPG have been implemented, for example to exploit the existence of biconnected components in the underlying graph.…”

Section: Scip-sdpmentioning

confidence: 99%

“…The improvements for SPG also have an immediate impact on problems that are transformed to SPG within SCIP-Jack, such as the group Steiner tree problem. Even for the Euclidean Steiner tree problem, large improvements are possible (the SPG can be used for full Steiner tree concatenation after the discretization of the problem): SCIP-Jack 2.0 is able to solve 19 Euclidean Steiner tree problems with up to 100 000 terminals for the first time to optimality, see Rehfeldt and Koch [87]. Notably, the state-of-the-art Euclidean Steiner tree solver GeoSteiner 5.1 [48] could not solve any of these instances even after one week of computation.…”

Section: Scip-sdpmentioning

confidence: 99%

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The SCIP Optimization Suite 8.0

Bestuzheva¹,

Besançon²,

Chen³

et al. 2021

Preprint

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The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 8.0 of the SCIP Optimization Suite. Major updates in SCIP include improvements in symmetry handling and decomposition algorithms, new cutting planes, a new plugin type for cut selection, and a complete rework of the way nonlinear constraints are handled. Additionally, SCIP 8.0 now supports interfaces for Julia as well as Matlab. Further, UG now includes a unified framework to parallelize all solvers, a utility to analyze computational experiments has been added to GCG, dual solutions can be postsolved by PaPILO, new heuristics and presolving methods were added to SCIP-SDP, and additional problem classes and major performance improvements are available in SCIP-Jack. Keywords Constraint integer programming • linear programming • mixed-integer linear programming • mixed-integer nonlinear programming • optimization solver • branch-andcut • branch-and-price • column generation • parallelization • mixed-integer semidefinite programming Mathematics Subject Classification 90C05 • 90C10 • 90C11 • 90C30 • 90C90 • 65Y05 * Extended author information is available at the end of the paper.

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Section: Scip-sdpmentioning

confidence: 99%

Section: Scip-sdpmentioning

confidence: 99%

Section: Scip-sdpmentioning

confidence: 99%

Section: Scip-sdpmentioning

confidence: 99%

See 2 more Smart Citations

The SCIP Optimization Suite 8.0

Bestuzheva¹,

Besançon²,

Chen³

et al. 2021

Preprint

Self Cite

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“…Simplifying the problem: reduction techniquesReduction techniques are a key ingredient for the exact solution of many N Phard optimization problems, such as Steiner tree(36) or vertex coloring(34). For QUBO, several reductions methods have been suggested in the literature.…”

mentioning

confidence: 99%

Faster exact solution of sparse MaxCut and QUBO problems

Rehfeldt¹,

Koch²,

Shinano³

2022

Preprint

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The maximum-cut problem is one of the fundamental problems in combinatorial optimization. With the advent of quantum computers, both the maximum-cut and the equivalent quadratic unconstrained binary optimization problem have experienced much interest in recent years.This article aims to advance the state of the art in the exact solution of both problems-by using mathematical programming techniques on digital computers. The main focus lies on sparse problem instances, although also dense ones can be solved. We enhance several algorithmic components such as reduction techniques and cutting-plane separation algorithms, and combine them in an exact branch-and-cut solver. Furthermore, we provide a parallel implementation. The new solver is shown to significantly outperform existing state-of-the-art software for sparse MaxCut and QUBO instances. Furthermore, we improve the best known bounds for several instances from the 7th DIMACS Challenge and the QPLIB, and solve some of them (for the first time) to optimality.

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Faster Algorithms for Steiner Tree and Related Problems: From Theory to Practice

Rehfeldt

2023

Lecture Notes in Operations Research

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Implications, Conflicts, and Reductions for Steiner Trees

Cited by 10 publications

References 23 publications

The SCIP Optimization Suite 8.0

The SCIP Optimization Suite 8.0

Faster exact solution of sparse MaxCut and QUBO problems

Faster Algorithms for Steiner Tree and Related Problems: From Theory to Practice

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