通过2-均值加速约束$k$ -均值
Speeding Up Constrained $k$-Means Through 2-Means
摘要：
对于约束2-均值问题，我们提出了一个$O\left(dn+d({1\overε})^{O({1\over ε})}\log n\right)$时间算法。它生成一个集合$U$的近似中心对$(c_1, c_2)$，使$U$中的一对可以诱导一个$(1+ε)$ -近似的问题。约束2-均值问题的现有近似方案需要$O(({1\overε})^{O({1\over ε})}dn)$时间，并且约束$k$ -均值问题的现有近似方案需要$O(({k\overε})^{O({k\over ε})}dn)$时间。利用本文提出的方法，我们指出，目前存在的约束$k$ -均值随时间的逼近格式$C(k, n, d, ε)$都可以转化为具有时间复杂度${C(k, n, d, ε)/ k^{Ω({1\overε})}}$的新的逼近格式.
英文摘要：
For the constrained 2-means problem, we present a $O\left(dn+d({1\overε})^{O({1\over ε})}\log n\right)$ time algorithm. It generates a collection $U$ of approximate center pairs $(c_1, c_2)$ such that one of pairs in $U$ can induce a $(1+ε)$-approximation for the problem. The existing approximation scheme for the constrained 2-means problem takes $O(({1\overε})^{O({1\over ε})}dn)$ time, and the existing approximation scheme for the constrained $k$-means problem takes $O(({k\overε})^{O({k\over ε})}dn)$ time. Using the method developed in this paper, we point out that every existing approximating scheme for the constrained $k$-means so far with time $C(k, n, d, ε)$ can be transformed to a new approximation scheme with time complexity ${C(k, n, d, ε)/ k^{Ω({1\overε})}}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
