2008, ISBN 9789812791443, xiii, 359

Book

IEEE Transactions on Computers, ISSN 0018-9340, 03/2015, Volume 64, Issue 3, pp. 818 - 831

Using insights from biological processes could help to design new optimization techniques for long-standing computational problems. This paper exploits a...

Steiner trees | Algorithm design and analysis | Biological system modeling | Computational modeling | Approximation algorithms | Steiner tree problem | Biology-inspired computing | network design | Optimization | physarum optimization | minimal exposure problem | DESIGN | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | COLONY | ENGINEERING, ELECTRICAL & ELECTRONIC | APPROXIMATION ALGORITHMS | ADAPTATION | SYSTEMS | WIRELESS SENSOR NETWORKS | AMEBOID ORGANISM | Trees (Graph theory) | Usage | Algorithms | Research | Mathematical optimization | Optimization techniques | Decision trees

Steiner trees | Algorithm design and analysis | Biological system modeling | Computational modeling | Approximation algorithms | Steiner tree problem | Biology-inspired computing | network design | Optimization | physarum optimization | minimal exposure problem | DESIGN | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | COLONY | ENGINEERING, ELECTRICAL & ELECTRONIC | APPROXIMATION ALGORITHMS | ADAPTATION | SYSTEMS | WIRELESS SENSOR NETWORKS | AMEBOID ORGANISM | Trees (Graph theory) | Usage | Algorithms | Research | Mathematical optimization | Optimization techniques | Decision trees

Journal Article

Networks, ISSN 0028-3045, 03/2019, Volume 73, Issue 2, pp. 206 - 233

The concept of reduction has frequently distinguished itself as a pivotal ingredient of exact solving approaches for the Steiner tree problem in graphs. In...

Steiner tree reductions | prize‐collecting Steiner tree problem | maximum‐weight connected subgraph problem | Steiner tree problem | rooted prize‐collecting Steiner tree problem | reduction techniques | maximum-weight connected subgraph problem | rooted prize-collecting Steiner tree problem | prize-collecting Steiner tree problem | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHM | Graphs | Reduction | Graph theory | Decision trees | Weight

Steiner tree reductions | prize‐collecting Steiner tree problem | maximum‐weight connected subgraph problem | Steiner tree problem | rooted prize‐collecting Steiner tree problem | reduction techniques | maximum-weight connected subgraph problem | rooted prize-collecting Steiner tree problem | prize-collecting Steiner tree problem | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHM | Graphs | Reduction | Graph theory | Decision trees | Weight

Journal Article

1992, Annals of discrete mathematics, ISBN 044489098X, Volume 53., xi, 339

Book

INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE, ISSN 0129-0541, 11/2017, Volume 28, Issue 7, pp. 869 - 887

We introduce and study a new Steiner tree problem variation called the bursty Steiner tree problem where new nodes arrive into bursts. This is an online...

approximation | Steiner tree | BOUNDS | online execution | COMPUTER SCIENCE, THEORY & METHODS | terminal Steiner tree | terminal bursts

approximation | Steiner tree | BOUNDS | online execution | COMPUTER SCIENCE, THEORY & METHODS | terminal Steiner tree | terminal bursts

Journal Article

Advances in Calculus of Variations, ISSN 1864-8258, 01/2016, Volume 9, Issue 1, pp. 19 - 39

The Steiner tree problem can be stated in terms of finding a connected set of minimal length containing a given set of finitely many points. We show how to...

rectifiable currents | chains | flat | 49Q15 | Steiner tree problem | calibration | 49Q20 | flat G-chains | MATHEMATICS | MATHEMATICS, APPLIED | FLAT CHAINS | METRIC SPACE | SETS | PARTITIONS | SOAP FILMS | FINITE PERIMETER | Decision trees | Optimization | Trees | Representations | Calibration | Mathematical analysis | Calculus of variations | Mathematics - Optimization and Control

rectifiable currents | chains | flat | 49Q15 | Steiner tree problem | calibration | 49Q20 | flat G-chains | MATHEMATICS | MATHEMATICS, APPLIED | FLAT CHAINS | METRIC SPACE | SETS | PARTITIONS | SOAP FILMS | FINITE PERIMETER | Decision trees | Optimization | Trees | Representations | Calibration | Mathematical analysis | Calculus of variations | Mathematics - Optimization and Control

Journal Article

Networks, ISSN 0028-3045, 01/2020, Volume 75, Issue 1, pp. 3 - 17

The Steiner tree problem (STP) is a classical NP‐hard combinatorial optimization problem with applications in computational biology and network wiring. The...

linear programming relaxation | mixed‐integer linear programming | extended formulation | Steiner tree | integrality gap | flow‐based formulation | flow-based formulation | mixed-integer linear programming | Wiring | Lower bounds | Apexes | Minimum cost | Linear programming | Graphs | Graph theory | Decision trees | Combinatorial analysis | Optimization

linear programming relaxation | mixed‐integer linear programming | extended formulation | Steiner tree | integrality gap | flow‐based formulation | flow-based formulation | mixed-integer linear programming | Wiring | Lower bounds | Apexes | Minimum cost | Linear programming | Graphs | Graph theory | Decision trees | Combinatorial analysis | Optimization

Journal Article

Networks, ISSN 0028-3045, 12/2016, Volume 68, Issue 4, pp. 331 - 339

Given a complete graph G = ( V , E ) , a positive length function on edges, and two subsets R of V and R ′ of R, the selected‐internal Steiner tree is defined...

bottleneck partial terminal Steiner tree problem | combinatorial optimization | bottleneck Steiner tree | facility allocation in networks | network design | bottleneck selected‐internal Steiner tree problem | bottleneck selected-internal Steiner tree problem | NUMBER | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | OPTICAL AMPLIFIERS | RATIO | NETWORKS | FULL | GRAPHS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | BOUNDS | APPROXIMATION ALGORITHM | Trees | Networks | Algorithms | Mathematical analysis | Graphs | Mathematical models | Graph theory | Terminals

bottleneck partial terminal Steiner tree problem | combinatorial optimization | bottleneck Steiner tree | facility allocation in networks | network design | bottleneck selected‐internal Steiner tree problem | bottleneck selected-internal Steiner tree problem | NUMBER | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | OPTICAL AMPLIFIERS | RATIO | NETWORKS | FULL | GRAPHS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | BOUNDS | APPROXIMATION ALGORITHM | Trees | Networks | Algorithms | Mathematical analysis | Graphs | Mathematical models | Graph theory | Terminals

Journal Article

9.
Full Text
Polyhedral results and a Branch-and-cut algorithm for the $$k$$ -cardinality tree problem

Mathematical Programming, ISSN 0025-5610, 12/2013, Volume 142, Issue 1, pp. 511 - 538

Given an undirected graph $$G$$ with vertex and edge weights, the $$k$$ -cardinality tree problem asks for a minimum weight tree of $$G$$ containing exactly...

Theoretical, Mathematical and Computational Physics | Mathematics | 90C27 | k$$ -Cardinality tree problem | Mathematical Methods in Physics | Polyhedral study | 90C35 | 90C57 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Combinatorics | Branch-and-cut algorithm | k-Cardinality tree problem | STEINER PROBLEM | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SEARCH | Algorithms

Theoretical, Mathematical and Computational Physics | Mathematics | 90C27 | k$$ -Cardinality tree problem | Mathematical Methods in Physics | Polyhedral study | 90C35 | 90C57 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Combinatorics | Branch-and-cut algorithm | k-Cardinality tree problem | STEINER PROBLEM | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SEARCH | Algorithms

Journal Article

Engineering Optimization, ISSN 0305-215X, 11/2019, Volume 51, Issue 11, pp. 1980 - 1996

This article introduces a novel method using mixed-integer linear programming for optimizing sewer layouts. The research concept was obtained from the...

sewer layout | Steiner minimal tree | mixed-integer linear programming | Optimization | Integrated circuits | Integer programming | Layouts | Circuit design | Linear programming | Cost analysis | Nodes | Construction costs | Design optimization

sewer layout | Steiner minimal tree | mixed-integer linear programming | Optimization | Integrated circuits | Integer programming | Layouts | Circuit design | Linear programming | Cost analysis | Nodes | Construction costs | Design optimization

Journal Article

Algorithmica, ISSN 0178-4617, 4/2013, Volume 65, Issue 4, pp. 868 - 884

Given a graph with n vertices, k terminals and positive integer weights not larger than c, we compute a minimum Steiner Tree in $\mathcal{O}^{\star}(2^{k}c)$...

Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Mathematics of Computing | Steiner tree | Computer Science | Inclusion-Exclusion | Polynomial space | Theory of Computation | Algorithm Analysis and Problem Complexity | Fixed parameter tractability | Exact algorithms

Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Mathematics of Computing | Steiner tree | Computer Science | Inclusion-Exclusion | Polynomial space | Theory of Computation | Algorithm Analysis and Problem Complexity | Fixed parameter tractability | Exact algorithms

Journal Article

European Journal of Operational Research, ISSN 0377-2217, 05/2020, Volume 283, Issue 1, pp. 1 - 15

•We focus on the generalized minimum spanning tree problem.•Some of the main known results relative to this problem are surveyed.•The paper is structured...

Combinatorial optimization | Survey | Generalized minimum spanning tree problem | DESIGN | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | problem | NEIGHBORHOOD SEARCH | Generalized minimum spanning tree | STEINER PROBLEMS | ALGORITHM

Combinatorial optimization | Survey | Generalized minimum spanning tree problem | DESIGN | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | problem | NEIGHBORHOOD SEARCH | Generalized minimum spanning tree | STEINER PROBLEMS | ALGORITHM

Journal Article

Applied Soft Computing Journal, ISSN 1568-4946, 11/2019, Volume 84

This study investigates a hierarchized Steiner tree problem in telecommunication networks. In such networks, users must be connected to capacitated hubs....

Co-evolutionary algorithms | Bi-level programming | Steiner tree problem | DESIGN | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | OPTIMIZATION | HEURISTICS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Co-evolutionary algorithms | Bi-level programming | Steiner tree problem | DESIGN | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | OPTIMIZATION | HEURISTICS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Journal Article

Evolutionary Computation, ISSN 1530-9304, 12/2017, Volume 25, Issue 4, pp. 707 - 723

The Steiner tree problem (STP) aims to determine some Steiner nodes such that the minimum spanning tree over these Steiner nodes and a given set of special...

Evolutionary algorithms | Multi-objective | Approximation ratio | Steiner tree | Computational complexity | approximation ratio | SEARCH | evolutionary algorithms | COMPLEXITY | TIME | COMPUTER SCIENCE, THEORY & METHODS | COMPUTATION | multi-objective | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | computational complexity | EXPECTED RUNTIMES | Approximation | Hypertext | Images | Graph theory | Empirical analysis | Genetic algorithms | Minimum weight | Mathematical analysis | Journals | Graphs | Decision trees | Heuristic

Evolutionary algorithms | Multi-objective | Approximation ratio | Steiner tree | Computational complexity | approximation ratio | SEARCH | evolutionary algorithms | COMPLEXITY | TIME | COMPUTER SCIENCE, THEORY & METHODS | COMPUTATION | multi-objective | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | computational complexity | EXPECTED RUNTIMES | Approximation | Hypertext | Images | Graph theory | Empirical analysis | Genetic algorithms | Minimum weight | Mathematical analysis | Journals | Graphs | Decision trees | Heuristic

Journal Article

European Journal of Operational Research, ISSN 0377-2217, 08/2017, Volume 261, Issue 1, pp. 54 - 66

•The framework considers connected facility location, (generalized) Steiner tree-star, rent-or-buy problems.•Dual ascent algorithm for asymmetric connected...

Connected facility location | Dual ascent | Benders decomposition | Combinatorial optimization | Branch-and-cut | STEINER PROBLEM | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | APPROXIMATION ALGORITHMS | Heuristic programming | Mathematical optimization | Analysis | Decomposition method | Computer Science | Operations Research

Connected facility location | Dual ascent | Benders decomposition | Combinatorial optimization | Branch-and-cut | STEINER PROBLEM | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | APPROXIMATION ALGORITHMS | Heuristic programming | Mathematical optimization | Analysis | Decomposition method | Computer Science | Operations Research

Journal Article

Computers and Operations Research, ISSN 0305-0548, 06/2018, Volume 94, pp. 38 - 51

•Four novel reliability measures for ring tree network design are proposed as an alternative for cost minimization.•We develop a generic ϵ-constraint method to...

Capacitated ring tree problem | Bi-objective optimization | Reliable network design | Telecommunications | Steiner tree | Mathematical programming | DESIGN | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MULTIOBJECTIVE NETWORK | ENGINEERING, INDUSTRIAL

Capacitated ring tree problem | Bi-objective optimization | Reliable network design | Telecommunications | Steiner tree | Mathematical programming | DESIGN | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MULTIOBJECTIVE NETWORK | ENGINEERING, INDUSTRIAL

Journal Article

European Journal of Operational Research, ISSN 0377-2217, 10/2018, Volume 270, Issue 2, pp. 419 - 429

•A fixed-parameter algorithm for the rectilinear travelling salesman problem.•A fixed-parameter algorithm for the rectilinear Steiner tree problem.•A refined...

Traveling salesman | Rectilinear Steiner tree problem | Fixed-parameter algorithm | Rectilinear traveling salesman problem | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | WAREHOUSE | TIME | Services | Usage | Graph theory | Sales personnel | Management | Computer Science | Operations Research

Traveling salesman | Rectilinear Steiner tree problem | Fixed-parameter algorithm | Rectilinear traveling salesman problem | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | WAREHOUSE | TIME | Services | Usage | Graph theory | Sales personnel | Management | Computer Science | Operations Research

Journal Article

Optimization Letters, ISSN 1862-4472, 03/2019, Volume 13, Issue 2, pp. 341 - 348

This paper studies a 4-approximation algorithm for k-prize collecting Steiner tree problems. This problem generalizes both k-minimum spanning tree problems and...

Primal-dual algorithm | Approximation algorithm | k-prize collecting traveling salesman problems | k-prize collecting Steiner tree problems | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Primal-dual algorithm | Approximation algorithm | k-prize collecting traveling salesman problems | k-prize collecting Steiner tree problems | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Journal Article

European Journal of Operational Research, ISSN 0377-2217, 09/2013, Volume 229, Issue 3, pp. 599 - 612

•The paper deals with the Robust PCStT, addressing interval uncertainty on its data.•Different mathematical programming formulations are...

Interval uncertainty | Mixed integer programming | Robust optimization | Prize collecting Steiner trees | Branch-and-cut | Steiner trees | Prize collecting | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PRICE | ALGORITHM | OPTIMIZATION | Robust statistics | Mathematical optimization | Analysis

Interval uncertainty | Mixed integer programming | Robust optimization | Prize collecting Steiner trees | Branch-and-cut | Steiner trees | Prize collecting | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PRICE | ALGORITHM | OPTIMIZATION | Robust statistics | Mathematical optimization | Analysis

Journal Article

Computers and Operations Research, ISSN 0305-0548, 07/2017, Volume 83, pp. 13 - 27

•We consider budget constrained network upgrading problems.•Lagrangian Relaxations and Branch-and-cut algorithms are designed.•Additional algorithmic...

Integer programming | Spanning tree problems | Lagrangian relaxation | COLLECTING STEINER PROBLEM | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ENGINEERING, INDUSTRIAL | Management science | Algorithms | Computer Science | Operations Research

Integer programming | Spanning tree problems | Lagrangian relaxation | COLLECTING STEINER PROBLEM | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ENGINEERING, INDUSTRIAL | Management science | Algorithms | Computer Science | Operations Research

Journal Article

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