Abstract
In this paper we study the problem of partitioning a convex polygon \(P\) with \(n\) vertices into \(m\) polygons of equal area and perimeter and give efficient algorithms for \(m = 2\) and for the more general case when \(m\) is a power of 2. While it was known such a partition exists, no algorithmic results were published so far. Our algorithm for \(m = 2\) is optimal and runs in \(O(n)\) time, while the algorithm for \(m = 2^k\), where \(k \ge 2\) is an integer, runs in \(O(n (2n)^{k-1})\) time. The algorithms have been implemented and tested on randomly generated convex polygons.
Daescu’s research has been partially supported by NSF award CNS1035460.
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© 2014 Springer International Publishing Switzerland
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Armaselu, B., Daescu, O. (2014). Algorithms for Fair Partitioning of Convex Polygons. In: Zhang, Z., Wu, L., Xu, W., Du, DZ. (eds) Combinatorial Optimization and Applications. COCOA 2014. Lecture Notes in Computer Science(), vol 8881. Springer, Cham. https://doi.org/10.1007/978-3-319-12691-3_5
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DOI: https://doi.org/10.1007/978-3-319-12691-3_5
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