Document Type

Technical Report

Publication Date


Technical Report Number


Faculty Approver

Deeparnab Chakrabarty


An instance of the k-center problem consists of n points in a metric space along with a positive integer k. The goal is to find the smallest radius r such that there exists a subset of k centers picked among them such that every point is within distance r of at least one center. Stuart Mentzer (Mentzer, 1988) wrote a paper showing that in the Euclidean plane, it is NP-Hard to approximate this problem up to a factor of √2 +√3 ≈ 1.93. However, his report is missing some details. In this note, we present details of his full construction.