Hanan grid explained

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

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

Notes and References

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