English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

In monotone submodular function maximization, approximation guarantees basedon the curvature of the objective function have been extensively studied in theliterature. However, the notion of curvature is often pessimistic, and werarely obtain improved approximation guarantees, even for very simple objectivefunctions.  In this paper, we provide a novel approximation guarantee by extracting anM$^\natural$-concave function $h:2^E \to \mathbb R_+$, a notion in discreteconvex analysis, from the objective function $f:2^E \to \mathbb R_+$. Weintroduce the notion of $h$-curvature, which measures how much $f$ deviatesfrom $h$, and show that we can obtain a $(1-\gamma/e-\epsilon)$-approximationto the problem of maximizing $f$ under a cardinality constraint in polynomialtime for any constant $\epsilon > 0$. Then, we show that we can obtainnontrivial approximation guarantees for various problems by applying theproposed algorithm.

A New Approximation Guarantee for Monotone Submodular Function Maximization via Discrete Convexity