On the existence of shortest networks in banach spaces

Bednov, B. B.; Strelkova, N. P.

doi:10.1134/s0001434613070043

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Uniqueness Of Steiner Minimal Tree1

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Cited by 8 publications

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“…In [30], it was shown that there exists a Banach space X, and for any n ≥ 3, a set A n of n points in X, such that there is no shortest network connecting A. The idea of the proof is to take the three-point set A 3 from [29] such that r 1 (A 3 ) is not attained and prove that for every set A n that is sufficiently close to A 3 in Hausdorff metric, there is no shortest network connecting A n .…”

Section: Uniqueness Of Steiner Minimal Treementioning

confidence: 99%

Current Open Problems in Discrete and Computational Geometry

Эдельсбруннер

Ivanov

Карасев

2015

Model. anal. inf. sist.

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We have selected problems that may not yet be well known, but have the potential to push the research in interesting directions. In particular, we state problems that do not require specific knowledge outside the standard circle of ideas in discrete geometry. Despite the relatively simple statements, these problems are related to current research and their solutions are likely to require new ideas and approaches. We have chosen problems from different fields to make this short paper attractive to a wide range of specialists.The article is published in the author’s wording.

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Section: Uniqueness Of Steiner Minimal Treementioning

confidence: 99%