Publication detail
Minimisation of Networks Based on Computational Geometry Data Structures
ŠEDA, M. ŠEDA, P.
Czech title
Minimalizace sítí založená na datových strukturách počítačové geometrie
English title
Minimisation of Networks Based on Computational Geometry Data Structures
Type
conference paper
Language
en
Original abstract
In this paper, we deal with a problem of finding the shortest connection of points placed in the Euclidean plane. The traditional strategy starts from the complete graph and finds its minimum spanning tree. However, this approach is proportional to the second power of the number of vertices, and therefore not very efficient. Additionally, if instead of the minimum spanning trees, minimum Steiner trees are considered, then the total length of the final network is decreased. Since the Steiner tree problem is NP-hard, in the case of large instances, heuristics must be used. Here, we propose a Delaunay triangulation-based deterministic heuristic and show that it gives very good results in short times.
Czech abstract
V tomto příspěvku se zabýváme problémem hledání nejkratšího spojení bodů umístěných v euklidovské rovině. Tradiční strategie začíná z úplného grafu a hledá k němu nejkratší kostru. Avšak složitost tohoto přístupu je úměrná druhé mocnině počtu vrcholů a není tedy příliš efektivní. Navíc pokud místo minimální kostry grafu uvažujeme minimální Steinerův strom, pak celková délka sítě se zkrátí. Protože Steinerův problém je NP-těžký, v případě velkých instancí je nutné použít heuristiky. V článku navrhujeme deterministickou heuristiku založenou na Delaunayho triangulaci a ukazujeme, že dává velmi dobré výsledky v krátkém čase.
English abstract
In this paper, we deal with a problem of finding the shortest connection of points placed in the Euclidean plane. The traditional strategy starts from the complete graph and finds its minimum spanning tree. However, this approach is proportional to the second power of the number of vertices, and therefore not very efficient. Additionally, if instead of the minimum spanning trees, minimum Steiner trees are considered, then the total length of the final network is decreased. Since the Steiner tree problem is NP-hard, in the case of large instances, heuristics must be used. Here, we propose a Delaunay triangulation-based deterministic heuristic and show that it gives very good results in short times.
Keywords in Czech
kostra grafu, Steinerův strom, NP-těžký problém, Voroného diagram, Delaunayho triangulace
Keywords in English
spanning tree, Steiner tree, NP-hard problem, heuristic, Voronoi diagram, Delaunay triangulation
Released
11.11.2018
Location
Moskva
ISBN
978-1-5386-9361-2
Book
2018 10th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT)
Pages from–to
143–147
Pages count
5
BIBTEX
@inproceedings{BUT149746,
author="Miloš {Šeda} and Pavel {Šeda},
title="Minimisation of Networks Based on Computational Geometry Data Structures",
booktitle="2018 10th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT)",
year="2018",
month="November",
pages="143--147",
address="Moskva",
isbn="978-1-5386-9361-2"
}