Minimal connections: the classical Steiner problem and generalizations

Authors

  • Emanuele Paolini Università di Firenze

DOI:

https://doi.org/10.6092/issn.2240-2829/3421

Keywords:

Steiner problem, minimal connections

Abstract

The classical Steiner problem is the problem of nding the shortest graph connecting a given finite set of points. In this seminar we review the classical problem and introduce a new, generalized formulation, which extends the original one to infinite sets in metric spaces.

References

[aMK34] V. Jarnk and M. Kossler. O minimalnch grafech, obsahujcch n danych bodu. Casopis propestovanmatematiky a fysiky, 063(8):223{235, 1934.

[CR41] R. Courant and Robbins. What Is Mathematics? Oxford Univ. Press, 1941.

[DHW87] Ding-Zhu Du, Frank K. Hwang, and J. F. Weng. Steiner minimal trees for regular polygons. Discrete & Computational Geometry, 2:65{84, 1987.

[FKH92] P. Winter F. K. Hwang, D. S. Richards. The Steiner tree problem. Elsevier Science Publisher B.V., 1992.

[IT94] A. O. Ivanov and A. A. Tuzhilin. Minimal networks: the Steiner problem and its generalizations. CRC Press, 1994.

[PS12] Emanuele Paolini and Eugene Stepanov. Existence and regularity results for the steiner problem. Calc. Var. Partial Di. Equations, 2012.

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Published

2012-12-30

How to Cite

Paolini, E. (2012). Minimal connections: the classical Steiner problem and generalizations. Bruno Pini Mathematical Analysis Seminar, 3(1), 72–87. https://doi.org/10.6092/issn.2240-2829/3421

Issue

Seminars 2012

Section

Articles

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Copyright (c) 2012 Emanuele Paolini

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