Pranjal Awasthi, Moses Charikar, Ravishankar Krishnaswamy, Ali Kemal Sinop
TL;DR本研究采用图谱分析的方法,证明了欧几里得 k-means 问题的近似难度对于所有的 k 和 d 都是 NP 难的,同时发现当前最佳难度结果可以被推广到三角免费图中。
Abstract
The Euclidean $k$-means problem is a classical problem that has been
extensively studied in the theoretical computer science, machine learning and
the computational geometry communities. In this problem, we are given a set of
$n$ points in Euclidean space $R^d$, and the goal is to choose $k$ centers in
$R^d$ so that the sum of squared distances of each point