# algorithms – Question in coreset construction fro K-median clustering

I was reading Ke chen’s paper about coreset construction for K-median clustering. In this paper, he assumed that $$A$$ is an $$(α, β)$$-bicriteria approximation for K-median clustering for some $$α, β=O(1)$$. I am wondering if the construction still work if $$A$$ is an arbitrary set of $$αk$$ centers?
Can anyone help prove the correctness of my suggestion?