On Unfolding Trees and Polygons on Various Lattices
نویسنده
چکیده
We consider the problem of unfolding lattice trees and polygons in hexagonal or triangular lattice in two dimensions. We show that a hexagonal/triangular lattice chain (resp. tree) can be straightened in O(n) (resp. O(n)) moves and time, and a hexagonal/triangular lattice polygon can be convexified in O(n) moves and time. We hope that the techniques we used shed some light on solving the more general conjecture that a unit tree in two dimensions can always be straightened.
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Zuni´c. On the maximal number of edges of convex digital polygons included into a square grid. A simplex variant solving an m ×d linear program in O (min(m 2 , d 2)) expected number of pivot steps. A simplex algorithm whose average number of steps is bounded between two quadratic functions of the smaller dimension. 12 P. K. Agarwal. A deterministic algorithm for partitioning arrangements of lin...
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