Simultaneous Approximation of Multi-criteria Submodular Function Maximization

Simultaneous approximation of multi-criteria submodular function maximization

Submodular Function Maximization

Submodularity is a property of set functions with deep theoretical consequences and far– reaching applications. At first glance it appears very similar to concavity, in other ways it resembles convexity. It appears in a wide variety of applications: in Computer Science it has recently been identified and utilized in domains such as viral marketing (Kempe et al., 2003), information gathering (Kr...

Improved Approximation Algorithms for k-Submodular Function Maximization

This paper presents a polynomial-time 1/2-approximation algorithm for maximizing nonnegative k-submodular functions. This improves upon the previous max{1/3, 1/(1+a)}-approximation by Ward and Živný [15], where a = max{1, √ (k − 1)/4}. We also show that for monotone ksubmodular functions there is a polynomial-time k/(2k− 1)-approximation algorithm while for any ε > 0 a ((k + 1)/2k + ε)-approxim...

Fast Multi-stage Submodular Maximization

Motivated by extremely large-scale machine learning problems, we introduce a new multistage algorithmic framework for submodular maximization (called MultGreed), where at each stage we apply an approximate greedy procedure to maximize surrogate submodular functions. The surrogates serve as proxies for a target submodular function but require less memory and are easy to evaluate. We theoreticall...

Robust Monotone Submodular Function Maximization

Instances of monotone submodular function maximization with cardinality constraint occur often in practical applications. One example is feature selection in machine learning, where in many models, adding a new feature to an existing set of features always improves the modeling power (monotonicity) and the marginal benefit of adding a new feature decreases as we consider larger sets (submodular...