A lower bound and two approximative algorithms for the K-partitioning of rectilinear polygons
This paper is about partitions that decompose a rectilinear polygon with n vertices (an n-gon) into rectilinear polygons with no more than k vertices each, where k is given and k<n. First we prove a lower bound L(P,k) for the number of components in the k-partition of a given n-gon P. Then two heuristic algorithms for the k-partitioning problem are presented. Their time complexities are O(n log2n) or O(n2log n), depending on the properties of the given n-gon. In most cases, both algorithms find k-partitions with no more than 2L(P,k) components.
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