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Generalizing Ham Sandwich Cuts to Equitable Subdivisions (2000)

Bespamyatnikh, S. ; Kirkpatrick, D. ; Snoeyink, J.

Springer

Discrete & computational geometry 24 (2000), S. 605-622

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ISSN: 1432-0444

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science , Mathematics

Notes: Abstract. We prove a generalization of the famous Ham Sandwich Theorem for the plane. Given gn red points and gm blue points in the plane in general position, there exists an equitable subdivision of the plane into g disjoint convex polygons, each of which contains n red points and m blue points. For g=2 this problem is equivalent to the Ham Sandwich Theorem in the plane. We also present an efficient algorithm for constructing an equitable subdivision.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s004540010065

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