1 research outputs found
Maximizing Non-monotone Submodular Set Functions Subject to Different Constraints: Combined Algorithms
We study the problem of maximizing constrained non-monotone submodular
functions and provide approximation algorithms that improve existing algorithms
in terms of either the approximation factor or simplicity. Our algorithms
combine existing local search and greedy based algorithms. Different
constraints that we study are exact cardinality and multiple knapsack
constraints. For the multiple-knapsack constraints we achieve a
-factor algorithm.
We also show, as our main contribution, how to use the continuous greedy
process for non-monotone functions and, as a result, obtain a -factor
approximation algorithm for maximization over any solvable down-monotone
polytope. The continuous greedy process has been previously used for maximizing
smooth monotone submodular function over a down-monotone polytope
\cite{CCPV08}. This implies a 0.13-approximation for several discrete problems,
such as maximizing a non-negative submodular function subject to a matroid
constraint and/or multiple knapsack constraints.Comment: There was an older version of the paper on arXiv. We update it to the
latest version. In particular, there was an error in the proof of Theorem 2.
We fixed it. The approximation remains the same as befor