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.

Hanan grid generated for a 5-terminal case

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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[1] Martin Zachariasen, A Catalog of Hanan Grid Problems Networks, vol. 38, 2000, pp. 200-221

[2] 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

[3] M. Hanan, On Steiner's problem with rectilinear distance, J. SIAM Appl. Math. 14 (1966), 255 - 265.