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Cited by 690

The DOI matches its Crossref record; 15 of the 15 references it cites were found in a registry or an index.

Steiner Minimal Trees

Gilbert, E. N., Pollak, H. O.·1968·SIAM Journal on Applied Mathematics
DOI 10.1137/0116001
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Abstract

A Steiner minimal tree for given points $A_1 , \cdots ,A_n $ in the plane is a tree which interconnects these points using lines of shortest possible total length. In order to achieve minimum length the Steiner minimal tree may contain other vertices (Steiner points) beside $A_1 , \cdots ,A_n $. We find conditions which simplify the task of constructing a Steiner minimal tree. Some of these use relationships with the easily constructed (ordinary) minimal tree which achieves minimum length among all trees having only $A_1 , \cdots ,A_n $ as vertices. Other questions concern the relative lengths of these two trees in extreme or typical cases. A review of the existing literature is included.

Overview

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Crossref · 10.1137/0116001

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15 of 15 references verified0 citation errors · 0 not checkable

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Citations

Cites

Show all 15 references

Research works printed but not linked: 8

  1. Courant Richard, 1941, What Is Mathematics?
  2. 10.2307/2688424 · doi:10.2307/2688424
  3. Loo-Keng Hua, 1962, Chinese Math., 2, 77
  4. Kuhn Harold W., 1966, J. Regional Science, 4, 21, 10.1111/j.1467-9787.1962.tb00902.x · doi:10.1111/j.1467-9787.1962.tb00902.x
  5. Maxwell J. C., 1864, Cambridge Philos. Mag.
  6. Maxwell J. C., 1869, Trans. Roy. Soc. Edinburgh, 26
  7. 10.2307/2689310 · doi:10.2307/2689310
  8. Weber Alfred, 1929, über den Standort der Industrien, Tübingen, 1909, Chap. III.

Cited by

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Metadata

Authors
Gilbert, E. N., & Pollak, H. O.
Venue
SIAM Journal on Applied Mathematics
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Published
1968-01
Volume
16
Issue
1
Pages
1-29
ISSN
  • 0036-1399
  • 1095-712X
DOI
10.1137/0116001
Cited by
690
References
15
Language
en

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CoChat. (2026). Citation check: Steiner Minimal Trees. https://app.cochat.ai/papers/10.1137/0116001
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Gilbert, E. N., & Pollak, H. O. (1968). Steiner Minimal Trees. SIAM Journal on Applied Mathematics. https://doi.org/10.1137/0116001

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.