# Hanan grid

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*.[1] It is named after Maurice Hanan, who was first[2] to investigate the rectilinear Steiner minimum tree and introduced this graph.[3]

## References

- Martin Zachariasen,
*A Catalog of Hanan Grid Problems**Networks*, vol. 38, 2000, pp. 200-221 - Christine R. Leverenz,
Miroslaw Truszczynski, The Rectilinear Steiner Tree Problem: Algorithms and Examples using Permutations of the Terminal Set,
*1999 ACM Southeast Regional Conference*, 1999, doi:10.1145/306363.306402 - M. Hanan, On Steiner's problem with rectilinear distance, J. SIAM Appl. Math. 14 (1966), 255 - 265.

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