We investigate two new optimization problems—minimizing a submodular function subject
to a submodular lower bound constraint (submodular cover) and maximizing a submodular …

We treat the text summarization problem as maximizing a submodular function under a
budget constraint. We show, both theoretically and empirically, a modified greedy algorithm …

We design new approximation algorithms for the problems of optimizing submodular and
supermodular functions subject to a single matroid constraint. Specifically, we consider the …

We introduce several generalizations of classical computer science problems obtained by
replacing simpler objective functions with general submodular functions. The new problems …

We consider the problem of maximizing a non-negative (possibly non-monotone)
submodular set function with or without constraints. Feige et al.[9] showed a 2/5 …

Submodular functions are a key concept in combinatorial optimization. Algorithms that
involve submodular functions usually assume that they are given by a (value) oracle. Many …

We present a practical and powerful new framework for both unconstrained and constrained
submodular function optimization based on discrete semidifferentials (sub-and super …

There has been much interest in the machine learning and algorithmic game theory
communities on understanding and using submodular functions. Despite this substantial …

We investigate three related and important problems connected to machine learning,
namely approximating a submodular function everywhere, learning a submodular function …

This paper addresses the problems of minimizing nonnegative submodular functions under
covering constraints, which generalize the vertex cover, edge cover, and set cover problems …