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Minimum Geometric Spanning Trees

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Encyclopedia of Algorithms

Years and Authors of Summarized Original Work

1999; Krznaric, Levcopoulos, Nilsson

Problem Definition

Let S be a set of n points in d-dimensional real space where d ≥ 1 is an integer constant. A minimum spanning tree (MST) of S is a connected acyclic graph with vertex set S of minimum total edge length. The length of an edge equals the distance between its endpoints under some metric. Under the so-called L p metric, the distance between two points x and y with coordinates (x 1, x 2, …, x d ) and (y 1, y 2, …, y d ), respectively, is defined as the pth root of the sum \(\sum \limits _{i=1}^{d}\left \vert x_{i} - y_{i}\right \vert ^{p}\).

Key Results

Since there is a very large number of papers concerned with geometric MSTs, only a few of them will be mentioned here.

In the common Euclidean L 2 metric, which simply measures straight-line distances, the MST problem in two dimensions can be solved optimally in time O(nlog n), by using the fact that the MST is a subgraph of the Delaunay...

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Recommended Reading

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Correspondence to Christos Levcopoulos .

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Levcopoulos, C. (2014). Minimum Geometric Spanning Trees. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-3-642-27848-8_236-2

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  • DOI: https://doi.org/10.1007/978-3-642-27848-8_236-2

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  • Online ISBN: 978-3-642-27848-8

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