Publication detail

Some Remarks to Proofs of Steiner Ratio for Rectilinear Steiner Trees

ŠEDA, M.

Czech title

Několik poznámek k důkazům Steinerova poměru pro rektilineární Steinerovy stromy

English title

Some Remarks to Proofs of Steiner Ratio for Rectilinear Steiner Trees

Type

journal article - other

Language

en

Original abstract

In this paper, we deal with rectilinear Steiner trees and their approximation by a rectilinear minimum spanning tree. It is known that the approximation ratio (called Steiner ratio) equals 1.50. In literature, several different proofs of this assertion can be found. We show that the proof presented in [7] is mistaken and propose its modification to prove the Steiner ratio correctly.

Czech abstract

V příspěvku se zabýváme rektilineárními Steinerovy stromy a jejich aproximací rektilineární kostrou grafu. Je známo, že aproximační poměr této aproximace (nazývaný Steinerův poměr) je roven 1.50. V literatuře lze najít několik odlišných důkazů tohoto tvrzení. Ukážeme zde, že důkaz prezentovaný v [7] je chybný a dále, jak jej třeba modifikovat, aby byl korektní.

English abstract

In this paper, we deal with rectilinear Steiner trees and their approximation by a rectilinear minimum spanning tree. It is known that the approximation ratio (called Steiner ratio) equals 1.50. In literature, several different proofs of this assertion can be found. We show that the proof presented in [7] is mistaken and propose its modification to prove the Steiner ratio correctly.

Keywords in English

rectilinear metric, Steiner tree, spanning tree, approximation, Steiner ratio

RIV year

2005

Released

01.04.2005

ISSN

1109-2769

Journal

WSEAS Transactions on Mathematics

Volume

4

Number

2

Pages count

7

BIBTEX


@article{BUT42792,
  author="Miloš {Šeda},
  title="Some Remarks to Proofs of Steiner Ratio for Rectilinear Steiner Trees",
  journal="WSEAS Transactions on Mathematics",
  year="2005",
  volume="4",
  number="2",
  month="April",
  issn="1109-2769"
}