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Hanan grid

Geometric grid created from horizontal and vertical lines drawn through each point in a set

Hanan grid
Summary

Geometric grid created from horizontal and vertical lines drawn through each point in a set

Hanan grid generated for a 5-terminal case

In geometry, the Hanan grid H(S) of a finite set S of points in the plane is obtained by constructing vertical and horizontal lines through each point in S.

The main motivation for studying the Hanan grid stems from the fact that it is known to contain a minimum length rectilinear Steiner tree for S. It is named after Maurice Hanan, who was firstChristine R. Leverenz, Miroslaw Truszczynski, The Rectilinear Steiner Tree Problem: Algorithms and Examples using Permutations of the Terminal Set, 1999 ACM Southeast Regional Conference, 1999, to investigate the rectilinear Steiner minimum tree and introduced this graph.

References

References

  1. Martin Zachariasen, ''[http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.43.3586 A Catalog of Hanan Grid Problems]'' ''Networks'', vol. 38, 2000, pp. 200-221
  2. M. Hanan, [http://amadeus.ecs.umass.edu/mie373/hanan_rsmt.pdf On Steiner's problem with rectilinear distance] {{Webarchive. link. (2016-03-04 , J. SIAM Appl. Math. 14 (1966), 255 - 265.)
Wikipedia Source

This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page.

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