An approximation algorithm for k-level squared metric facility location problem with outliers

We investigate k-level squared metric facility location problem with outliers (k-SMFLPWO) for any constant k. In k-SMFLPWO, given k facilities set \({\mathcal {F}}_{l}\), where \(l\in \{1, 2, \cdots , k\}\), clients set \({\mathcal {C}}\) with cardinality n and a non-negative integer \(q<n\). The sum of opening and connection cost will be substantially increased by distant clients. To minimize the total cost, some distant clients can not be connected, in short, at least \(n-q\) clients in clients set \({\mathcal {C}}\) are connected to the path \(p=(i_{1}\in {\mathcal {F}}_{1}, i_{2}\in {\mathcal {F}}_{2}, \cdots , i_{k}\in {\mathcal {F}}_{k})\) where the facilities in path p are opened. Based on primal-dual approximation algorithm and the property of squared metric triangle inequality, we present a constant factor approximation algorithm for k-SMFLPWO.