Steiner Tree Problems in VLSI Layout Designs

Cho, Jun-Dong

doi:10.1007/978-1-4613-0255-1_4

Cited by 4 publications

(3 citation statements)

References 25 publications

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“…Their code is publicly available. Many problem variants involving more realistic side constraints (such as avoiding obstacles, or additionally minimizing flow‐costs) were also addressed in the literature [35, 51, 244].…”

Section: Old and New Applications Of The Stpmentioning

confidence: 99%

“…The Steiner tree problem (STP) in graphs is among the most prominent problems in the history of combinatorial optimization. It plays a central role in network design problems, design of integrated circuits, location problems [46, 51, 134, 156, 200] and more recently even in machine learning, systems biology, and bioinformatics [8, 136, 207, 221].…”

Section: Introductionmentioning

confidence: 99%

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Solving Steiner trees: Recent advances, challenges, and perspectives

Ljubić

2020

Networks

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The Steiner tree problem (STP) in graphs is one of the most studied problems in combinatorial optimization. Since its inception in 1970, numerous articles published in the journal Networks have stimulated new theoretical and computational studies on Steiner trees: from approximation algorithms, heuristics, metaheuristics, all the way to exact algorithms based on (mixed) integer linear programming, fixed parameter tractability, or combinatorial branch‐and‐bounds. The pervasive applicability and relevance of Steiner trees have been reinforced by the recent 11th DIMACS Implementation Challenge in 2014 and the PACE 2018 Challenge. This article provides an overview of the rich developments from the last three decades for the STP in graphs and highlights the most recent computational studies for some of its closely related variants.

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Section: Old and New Applications Of The Stpmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Solving Steiner trees: Recent advances, challenges, and perspectives

Ljubić

2020

Networks

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“…It is known that the Steiner tree problem in graphs is NP-Hard [6], so proposals for new heuristics helps the development of better approximation algorithms. The Steiner tree problem in graphs has many practical applications in the design of transport, electrical and computer networks [2,5]. In Table 1, we present the state-of-the-art of exact and approximative algorithms for the Steiner tree problem, with their time complexity and the approximation ratio.…”

Section: Introductionmentioning

confidence: 99%

An algorithmic strategy to select vertices as router candidates in a Steiner tree

Martinez,

de Freitas,

da Silva

et al. 2020

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The Steiner tree problem in graphs is NP-Hard, so the development of algorithms that provide good polynomial-time solutions are desired. In this paper, we present a heuristic algorithm based on the concepts of an efficient exact enumerative algorithm proposed by Dourado et al (2014). Despite the existence of several approximation algorithms for this problem, we present a simple heuristic method and show that it achieves competitive results on benchmark instances from the literature, with an empirical average approximation ratio of no more than 1.01% and a maximum of 1.12%.

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A Physarum-inspired approach to the Euclidean Steiner tree problem

Hsu

Massolo

Schaposnik

2022

Sci Rep

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This paper presents a novel biologically-inspired explore-and-fuse approach to solving a large array of problems. The inspiration comes from Physarum, a unicellular slime mold capable of solving the traveling salesman and Steiner tree problems. Besides exhibiting individual intelligence, Physarum can also share information with other Physarum organisms through fusion. These characteristics of Physarum imply that spawning many such organisms we can explore the problem space in parallel, each individual gathering information and forming partial solutions pertaining to a local region of the problem space. When the organisms meet, they fuse and share information, eventually forming one organism which has a global view of the problem and can apply its intelligence to find an overall solution to the problem. This approach can be seen as a “softer” method of divide and conquer. We demonstrate this novel approach, developing the Physarum Steiner Algorithm which is capable of finding feasible solutions to the Euclidean Steiner tree problem. This algorithm is of particular interest due to its resemblance to Physarum polycephalum, ability to leverage parallel processing, avoid obstacles, and operate on various shapes and topological surfaces including the rectilinear grid.

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Steiner Tree Problems in VLSI Layout Designs

Cited by 4 publications

References 25 publications

Solving Steiner trees: Recent advances, challenges, and perspectives

Solving Steiner trees: Recent advances, challenges, and perspectives

An algorithmic strategy to select vertices as router candidates in a Steiner tree

A Physarum-inspired approach to the Euclidean Steiner tree problem

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