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/

Global: Zendy Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Submodularity is a key property in discrete optimization. Submodularity hasbeen widely used for analyzing the greedy algorithm to give performance boundsand providing insight into the construction of valid inequalities formixed-integer programs. In recent years, researchers started to studyapproximate submodularity, with a primary focus on providing performance boundsfor iterative approaches. In this paper, we study approximate submodularityfrom a different perspective in order to broaden its use cases in discreteoptimization. We define metrics that quantify approximate submodularity, whichwe then use to derive new properties about both approximate submodularitypreservation and the well-known Lov\'{a}sz extension for set functions. We alsoshow that previous analyses of mixed-integer sets, such as the submodularknapsack polytope, can be extended to the approximate submodularity setting.Our work demonstrates that one may generalize many of the analytical tools usedin submodular optimization into the approximate submodularity context.

Approximate Submodularity and Its Implications in Discrete Optimization