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.

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