A Survey on Exact and Approximation Algorithms for Clustering
نویسنده
چکیده
Given a set of point P in Rd, a clustering problem is to partition P into k subsets {P1, P2, · · · , Pk} in such a way that a given objective function is minimized. The most studied cost functions for a cluster, μ(Pi), are maximum or average radius of Pi, maximum diameter of Pi, and maximum width of Pi. The overall objective function is ⊕ μ(Pi), where ⊕ is typically the Lp-norm operator. The most common operators are the L1 (sum) and L∞ (max) norms. This project consists of two parts: The first part is a survey on the min max and min sum clustering problems. This includes 1-center, k-center, k-line center, k-slab cover, k-median, facility location, and k-clustering that minimizes the sum of cluster diameters. In the second part, we will study the clustering problem which objective is to minimize the sum of volume of k axis-aligned rectangles subject to the constraints that all points are covered by at least one rectangle.
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