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

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, doi:10.1145/306363.306402
  3. ^ M. Hanan, On Steiner’s problem with rectilinear distance, J. SIAM Appl. Math. 14 (1966), 255 - 265.