Computing the shortest network under a fixed topology

Guoliang Xue, K. Thulasiraman

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We show that, in any given uniform orientation metric plane, the shortest network interconnecting a given set of points under a fixed topology can be computed by solving a linear programming problem whose size is bounded by a polynomial in the number of terminals and the number of legal orientations. When the given topology is restricted to a Steiner topology, our result implies that the Steiner minimum tree under a given Steiner topology can be computed in polynomial time in any given uniform orientation metric with λ legal orientations for any fixed integer λ ≥ 2. This settles an open problem posed in a recent paper.

Original languageEnglish (US)
Pages (from-to)1117-1120
Number of pages4
JournalIEEE Transactions on Computers
Volume51
Issue number9
DOIs
StatePublished - Sep 2002

Fingerprint

Topology
Computing
Polynomials
Metric
Trees (mathematics)
Linear programming
Set of points
Open Problems
Polynomial time
Imply
Polynomial
Integer

Keywords

  • Linear programming
  • Shortest network under a fixed topology
  • Steiner trees
  • Uniform orientation metric plane

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Hardware and Architecture

Cite this

Computing the shortest network under a fixed topology. / Xue, Guoliang; Thulasiraman, K.

In: IEEE Transactions on Computers, Vol. 51, No. 9, 09.2002, p. 1117-1120.

Research output: Contribution to journalArticle

Xue, Guoliang ; Thulasiraman, K. / Computing the shortest network under a fixed topology. In: IEEE Transactions on Computers. 2002 ; Vol. 51, No. 9. pp. 1117-1120.
@article{9fe3db76c88144a5a66d180d38126ded,
title = "Computing the shortest network under a fixed topology",
abstract = "We show that, in any given uniform orientation metric plane, the shortest network interconnecting a given set of points under a fixed topology can be computed by solving a linear programming problem whose size is bounded by a polynomial in the number of terminals and the number of legal orientations. When the given topology is restricted to a Steiner topology, our result implies that the Steiner minimum tree under a given Steiner topology can be computed in polynomial time in any given uniform orientation metric with λ legal orientations for any fixed integer λ ≥ 2. This settles an open problem posed in a recent paper.",
keywords = "Linear programming, Shortest network under a fixed topology, Steiner trees, Uniform orientation metric plane",
author = "Guoliang Xue and K. Thulasiraman",
year = "2002",
month = "9",
doi = "10.1109/TC.2002.1032631",
language = "English (US)",
volume = "51",
pages = "1117--1120",
journal = "IEEE Transactions on Computers",
issn = "0018-9340",
publisher = "IEEE Computer Society",
number = "9",

}

TY - JOUR

T1 - Computing the shortest network under a fixed topology

AU - Xue, Guoliang

AU - Thulasiraman, K.

PY - 2002/9

Y1 - 2002/9

N2 - We show that, in any given uniform orientation metric plane, the shortest network interconnecting a given set of points under a fixed topology can be computed by solving a linear programming problem whose size is bounded by a polynomial in the number of terminals and the number of legal orientations. When the given topology is restricted to a Steiner topology, our result implies that the Steiner minimum tree under a given Steiner topology can be computed in polynomial time in any given uniform orientation metric with λ legal orientations for any fixed integer λ ≥ 2. This settles an open problem posed in a recent paper.

AB - We show that, in any given uniform orientation metric plane, the shortest network interconnecting a given set of points under a fixed topology can be computed by solving a linear programming problem whose size is bounded by a polynomial in the number of terminals and the number of legal orientations. When the given topology is restricted to a Steiner topology, our result implies that the Steiner minimum tree under a given Steiner topology can be computed in polynomial time in any given uniform orientation metric with λ legal orientations for any fixed integer λ ≥ 2. This settles an open problem posed in a recent paper.

KW - Linear programming

KW - Shortest network under a fixed topology

KW - Steiner trees

KW - Uniform orientation metric plane

UR - http://www.scopus.com/inward/record.url?scp=0036709609&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036709609&partnerID=8YFLogxK

U2 - 10.1109/TC.2002.1032631

DO - 10.1109/TC.2002.1032631

M3 - Article

AN - SCOPUS:0036709609

VL - 51

SP - 1117

EP - 1120

JO - IEEE Transactions on Computers

JF - IEEE Transactions on Computers

SN - 0018-9340

IS - 9

ER -