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

We consider the computational versions of the Erd\H os-Szekeres theorem andrelated problems in 3 dimensions. We show that, in constrast to the planarcase, no polynomial time algorithm exists for determining the largest (empty)convex subset (unless P=NP) among a set of points, by proving that thecorresponding decision problem is NP-hard. This answers a question by Dobkin,Edelsbrunner and Overmars from 1990.  As a corollary, we derive a similar result for the closely related problem oftesting weak epsilon-nets in R^3. Answering a question by Chazelle et al. from1995, our reduction shows that the problem is co-NP-hard.  This is work in progress - we are still trying to find a smart approximationalgorithm for the problems.

Erd\H{o}s-Szekeres and Testing Weak epsilon-Nets are NP-hard in 3 dimensions - and what now?