Maximizing a Monotone Submodular Function Subject to a Matroid Constraint

• Published in: SIAM journal on computing Vol. 40; no. 6; pp. 1740 - 1766
• Main Authors: Calinescu, Gruia, Chekuri, Chandra, Pál, Martin, Vondrák, Jan
• Format: Journal Article
• Language: English
• Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2011
• Subjects: Algorithms; Approximation; Assignment problem; Computer science; Graphs

Let $f:2^X \rightarrow \cal R_+$ be a monotone submodular set function, and let $(X,\cal I)$ be a matroid. We consider the problem ${\rm max}_{S \in \cal I} f(S)$. It is known that the greedy algorithm yields a $1/2$-approximation [M. L. Fisher, G. L. Nemhauser, and L. A. Wolsey, Math. Programming S...