On the Optimal Bisection of a Polygon

نویسندگان

  • Elias Koutsoupias
  • Christos H. Papadimitriou
  • Martha Sideri
چکیده

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 nds a subdivision into two parts with total perimeter at most that of the optimum bisection, such that the two parts have areas within of each other; the time is polynomial in the number of sides of the polygon, and 1. 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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عنوان ژورنال:
  • INFORMS Journal on Computing

دوره 4  شماره 

صفحات  -

تاریخ انتشار 1992