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Rectilinear Spanning Tree

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  • First Online:
Encyclopedia of Algorithms

  • 261 Accesses

Years and Authors of Summarized Original Work

.

  • 2001; Zhou, Shenoy, Nicholls

Problem Definition

Given a set of n points in a plane, a spanning tree is a set of edges that connects all the points and contains no cycles. When each edge is weighted using some distance metric of the incident points, the metric minimum spanning tree is a tree whose sum of edge weights is minimum. If the Euclidean distance (L2) is used, it is called the Euclidean minimum spanning tree; if the rectilinear distance (L1) is used, it is called the rectilinear minimum spanning tree.

Since the minimum spanning tree problem on a weighted graph is well studied, the usual approach for metric minimum spanning tree is to first define a weighted graph on the set of points and then to construct a spanning tree on it.

Rectilinear Spanning Tree, Fig. 1
figure 1821 figure 1821

Octal partition and the uniqueness property

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Recommended Reading

  1. McCreight EM (1985) Priority search trees. SIAM J Comput 14:257–276

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  2. Pugh W (1990) Skip lists: a probabilistic alternative to balanced trees. Commun ACM 33:668–676

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  3. Robins G, Salowe JS (1995) Low-degree minimum spanning tree. Discret Comput Geom 14:151–165

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  4. Zheng SQ, Lim JS, Iyengar SS (1996) Finding obstacle-avoiding shortest paths using implicit connection graphs. IEEE Trans Comput Aided Des 15:103–110

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  5. Zhou H, Shenoy N, Nicholls W (2001) Efficient minimum spanning tree construction without delaunay triangulation. In: Proceedings of Asian and South Pacific design automation conference, Yokohama

    Book  MATH  Google Scholar 

  6. Zhou H, Shenoy N, Nicholls W (2002) Efficient spanning tree construction without delaunay triangulation. Inf Proc Lett 81:271–276

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Author information

Authors and Affiliations

  1. Electrical Engineering and Computer Science (EECS) Department, Northwestern University, 633 Clark Street, 60208, Evanston, IL, USA

    Hai Zhou

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  1. Hai Zhou
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Correspondence to Hai Zhou .

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Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Zhou, H. (2016). Rectilinear Spanning Tree. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_336

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