Titlebook: Automata, Languages, and Programming; 39th International C Artur Czumaj,Kurt Mehlhorn,Roger Wattenhofer Conference proceedings 2012 Springe

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Approximation Algorithms for Online Weighted Rank Function Maximization under Matroid Constraintsatroid is defined. The goal is to incrementally choose a subset that remains independent in the matroid over time. At each time, a new weighted rank function of a different matroid (one per time) over the same elements is presented; the algorithm can add a few elements to the incrementally construct

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Sparse Fault-Tolerant Spanners for Doubling Metrics with Bounded Hop-Diameter or Degree, if for any subset .???. with |.|?≤?., it holds that ..(., .)?≤?. ·.(., .), for any pair of ., .?∈?.???...For any doubling metric, we give a basic construction of .-VFTS with stretch arbitrarily close to 1 that has optimal .(.) edges. In addition, we also consider bounded hop-diameter, which is stu

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Efficient Submodular Function Maximization under Linear Packing Constraints when the number of constraints is constant or when the width of the constraints is sufficiently large. This motivates us to study the large width setting, trying to determine its exact approximability. We develop an algorithm that has an approximation ratio of (1???.)(1???1/.) when .?=?Ω(ln . / ..)