
An Approximation Algorithm for Covering Linear Programs and its Application to BinPacking
We give an α(1+ϵ)approximation algorithm for solving covering LPs, assu...
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Improved LPbased Approximation Algorithms for Facility Location with Hard Capacities
We present LPbased approximation algorithms for the capacitated facilit...
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Approximation Algorithms for Socially Fair Clustering
We present an (e^O(p)logℓ/loglogℓ)approximation algorithm for socially ...
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Geometry Meets Vectors: Approximation Algorithms for Multidimensional Packing
We study the generalized multidimensional bin packing problem (GVBP) tha...
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Approximation Algorithms for the Bottleneck Asymmetric Traveling Salesman Problem
We present the first nontrivial approximation algorithm for the bottlene...
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Approximate MultiMatroid Intersection via Iterative Refinement
We introduce a new iterative rounding technique to round a point in a ma...
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NearlyLinear Time Approximate Scheduling Algorithms
We study nearlylinear time approximation algorithms for nonpreemptive ...
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Maximum Coverage with Cluster Constraints: An LPBased Approximation Technique
Packing problems constitute an important class of optimization problems, both because of their high practical relevance and theoretical appeal. However, despite the large number of variants that have been studied in the literature, most packing problems encompass a single tier of capacity restrictions only. For example, in the Multiple Knapsack Problem, we assign items to multiple knapsacks such that their capacities are not exceeded. But what if these knapsacks are partitioned into clusters, each imposing an additional capacity restriction on the knapsacks contained in that cluster? In this paper, we study the Maximum Coverage Problem with Cluster Constraints (MCPC), which generalizes the Maximum Coverage Problem with Knapsack Constraints (MCPK) by incorporating cluster constraints. Our main contribution is a general LPbased technique to derive approximation algorithms for cluster capacitated problems. Our technique allows us to reduce the cluster capacitated problem to the respective original packing problem. By using an LPbased approximation algorithm for the original problem, we can then obtain an effective rounding scheme for the problem, which only loses a small fraction in the approximation guarantee. We apply our technique to derive approximation algorithms for MCPC. To this aim, we develop an LPbased 1/2(11/e)approximation algorithm for MCPK by adapting the pipage rounding technique. Combined with our reduction technique, we obtain a 1/3(11/e)approximation algorithm for MCPC. We also derive improved results for a special case of MCPC, the Multiple Knapsack Problem with Cluster Constraints (MKPC). Based on a simple greedy algorithm, our approach yields a 1/3approximation algorithm. By combining our technique with a more sophisticated iterative rounding approach, we obtain a 1/2approximation algorithm for certain special cases of MKPC.
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