AI 中文总结
针对带离群点的加权超度量嵌入问题，提出使用O(n^5)次运算的确定性5/2近似算法，改进了此前3的近似因子，同时证明该问题在严格小于2的因子下近似是UGC难的。
AI 中文摘要
带离群点的加权超度量嵌入问题要求找出权重最小的点集，删除这些点后剩余的度量空间成为超度量，等价于不存在具有唯一最大距离的三元组。我们提出了一种确定性的5/2近似算法，使用O(n^5)次算术和比较运算，改进了此前针对任意非负顶点权重的3近似因子。在任意严格小于2的因子下近似该问题是UGC难的。
英文摘要
Weighted ultrametric embedding with outliers asks for a minimum weight set of points whose deletion makes the remaining metric an ultrametric, equivalently, leaves no triple with a unique largest distance. We give a deterministic $5/2$-approximation using $O(n^5)$ arithmetic and comparison operations, improving the previous factor $3$ for arbitrary nonnegative vertex weights. Approximating the problem within any factor strictly below $2$ is UGC-hard.
Comments11 pages
