Reference Work Entry

Encyclopedia of Algorithms

pp 1-99

# Local Search for K-medians and Facility Location

2001; Arya, Garg, Khandekar, Meyerson, Munagala, Pandit
• Kamesh MunagalaAffiliated withLevine Science Research Center, Duke University

## Keywords and Synonyms

k-Medians; k-Means; k-Medioids; Facility location; Point location; Warehouse location; Clustering

## Problem Definition

Clustering is a form of unsupervised learning, where the goal is to “learn” useful patterns in a data set $${ \mathcal{D} }$$ of size n. It can also be thought of as a data compression scheme where a large data set is represented using a smaller collection of “representatives”. Such a scheme is characterized by specifying the following:

1. 1.

distance metric $${ \mathbf{d} }$$ between items in the data set. This metric should satisfy the triangle inequality: $${ \mathbf{d}(i,j) \le \mathbf{d}(j,k) + \mathbf{d}(k,i) }$$ for any three items $${ i,j,k \in \mathcal{D} }$$. In addition, $${ \mathbf{d}(i,j) = \mathbf{d}(j,i) }$$ for all $${ i,j \in \mathcal{S} }$$ and $${ \mathbf{d}(i,i) = 0 }$$. Intuitively, if the distance between two items is small ...

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