Autoren:	Althaus, Ernst Rauterberg, Felix Ziegler, Sarah
Titel:	Computing Euclidean Steiner trees over segments
Online-Publikationsdatum:	11-Mai-2021
Erscheinungsdatum:	2020
Sprache des Dokuments:	Englisch
Zusammenfassung/Abstract:	In the classical Euclidean Steiner minimum tree (SMT) problem, we are given a set of points in the Euclidean plane and we are supposed to find the minimum length tree that connects all these points, allowing the addition of arbitrary additional points. We investigate the variant of the problem where the input is a set of line segments. We allow these segments to have length 0, i.e., they are points and hence we generalize the classical problem. Furthermore, they are allowed to intersect such that we can model polygonal input. As in the GeoSteiner approach of Juhl et al. (Math Program Comput 10(2):487–532, 2018) for the classical case, we use a two-phase approach where we construct a superset of so-called full components of an SMT in the first phase. We prove a structural theorem for these full components, which allows us to use almost the same GeoSteiner algorithm as in the classical SMT problem. The second phase, the selection of a minimal cost subset of constructed full components, is exactly the same as in GeoSteiner approach. Finally, we report some experimental results that show that our approach is more efficient than the approximate solution that is obtained by sampling the segments.
DDC-Sachgruppe:	004 Informatik 004 Data processing 510 Mathematik 510 Mathematics
Veröffentlichende Institution:	Johannes Gutenberg-Universität Mainz
Organisationseinheit:	FB 08 Physik, Mathematik u. Informatik
Veröffentlichungsort:	Mainz
ROR:	https://ror.org/023b0x485
DOI:	http://doi.org/10.25358/openscience-5792
Version:	Published version
Publikationstyp:	Zeitschriftenaufsatz
Weitere Angaben zur Dokumentart:	Scientific article
Nutzungsrechte:	CC BY
Informationen zu den Nutzungsrechten:	https://creativecommons.org/licenses/by/4.0/
Zeitschrift:	EURO journal on computational optimization 8
Seitenzahl oder Artikelnummer:	309 325
Verlag:	Springer
Verlagsort:	Berlin u.a.
Erscheinungsdatum:	2020
ISSN:	2192-4414
URL der Originalveröffentlichung:	https://doi.org/10.1007/s13675-020-00125-w
DOI der Originalveröffentlichung:	10.1007/s13675-020-00125-w
Enthalten in den Sammlungen:	JGU-Publikationen