Separating k -sc Median from the Supplier Version

Aditya Anand, Euiwoong Lee

Abstract: Given a metric space (V, d) along with an integer k, the \(k\text {-}\textsc {Median}\) problem asks to open k centers \(C \subseteq V\) to minimize \(\sum _{v \in V} d(v, C)\), where \(d(v, C) := \min _{c \in C} d(v, c)\). While the best-known approximation ratio 2.613 holds for the more general supplier version where an additional set \(F \subseteq V\) is given with the restriction \(C \subseteq F\), the best known hardness for these two versions are \(1+1/e \approx 1.36\) and \(1+2/e \approx 1.73\) respectively, using the same reduction from \(\textsc {Maximum}~k\text {-}\textsc {Coverage} \). We prove the following two results separating them.