Few Cuts Meet Many Point Sets

08/09/2018

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We study the problem of how to breakup many point sets in R^d into smaller parts using a few splitting (shared) hyperplanes. This problem is related to the classical Ham-Sandwich Theorem. We provide a logarithmic approximation to the optimal solution using the greedy algorithm for submodular optimization.

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Few Cuts Meet Many Point Sets

Deterministic (1/2 + ε)-Approximation for Submodular Maximization over a Matroid

Distributed Maximization of Submodular and Approximately Submodular Functions

Practical Budgeted Submodular Maximization

Non-Monotone Submodular Maximization with Multiple Knapsacks in Static and Dynamic Settings

Determinantal Point Processes Stochastic Approximation for Combinatorial Optimization

Comments on the proof of adaptive submodular function minimization

Composable Core-sets for Determinant Maximization: A Simple Near-Optimal Algorithm

Few Cuts Meet Many Point Sets

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Deterministic (1/2 + ε)-Approximation for Submodular Maximization over a Matroid

Distributed Maximization of Submodular and Approximately Submodular Functions

Practical Budgeted Submodular Maximization

Non-Monotone Submodular Maximization with Multiple Knapsacks in Static and Dynamic Settings

Determinantal Point Processes Stochastic Approximation for Combinatorial Optimization

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