E. Koutsoupias, C. H. Papadimitriou, and M. Sideri.
On the optimal bisection of a polygon.
ORSA Journal on Computing, 4(4):435--438, Fall 1992.
Abstract
We show that bisecting a polygon into two equal (possibly disconnected) parts with the smallest possible total perimeter is NP-complete, and it is in fact NP-hard to approximate within any ratio.In contrast, we give a dynamic programming algorithm which finds a subdivision into two parts with total perimeter at most that of the optimum bisection, such that the two parts have areas within $\epsilon$ of each other; the time is polynomial in the number of sides of the polygon, and $1\over \epsilon$.When the polygon is convex, or if the parts are required to be connected, then the exact problem can be solved in quadratic time.Bib
@Article{KPS92,
author = {E. Koutsoupias and C. H. Papadimitriou and M. Sideri},
title = {On the optimal bisection of a polygon},
journal = {ORSA Journal on Computing},
year = 1992,
month = {Fall},
volume = 4,
number = 4,
pages = {435--438}
}
@InProceedings{KPS90,
author = {E. Koutsoupias and C. H. Papadimitriou and M. Sideri},
title = {On the optimal bisection of a polygon},
booktitle = {Proceedings of the Sixth Annual Symposium on Computational Geometry},
year = 1990,
month = {6--8 } # jun,
pages = {198--202},
address = {Berkeley, California}}