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We study the Capacitated k-Median problem, for which all the known constant factor approximation algorithms violate either the number of facilities or the capacities. While the standard LP-relaxation can only be used for algorithms violating one of the two by a factor of at least two, Shi Li [SODA15, SODA16] gave algorithms violating the number of facilities by a factor of 1+{epsilon} exploring properties of extended relaxations. In this paper we develop a constant factor approximation algorithm for Uniform Capacitated k-Median violating only the capacities by a factor of 1+{epsilon}. The algorithm is based on a configuration LP. Unlike in the algorithms violating the number of facilities, we cannot simply open extra few facilities at selected locations. Instead, our algorithm decides about the facility openings in a carefully designed dependent rounding process.
The $k$-Facility Location problem is a generalization of the classical problems $k$-Median and Facility Location. The goal is to select a subset of at most $k$ facilities that minimizes the total cost of opened facilities and established connections
This study considers the (soft) capacitated vertex cover problem in a dynamic setting. This problem generalizes the dynamic model of the vertex cover problem, which has been intensively studied in recent years. Given a dynamically changing vertex-wei
In this paper we initiate the study of the heterogeneous capacitated $k$-center problem: given a metric space $X = (F cup C, d)$, and a collection of capacities. The goal is to open each capacity at a unique facility location in $F$, and also to assi
We present a packing-based approximation algorithm for the $k$-Set Cover problem. We introduce a new local search-based $k$-set packing heuristic, and call it Restricted $k$-Set Packing. We analyze its tight approximation ratio via a complicated comb
Let $G=(V, E)$ be a given edge-weighted graph and let its {em realization} $mathcal{G}$ be a random subgraph of $G$ that includes each edge $e in E$ independently with probability $p$. In the {em stochastic matching} problem, the goal is to pick a sp