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 classic cake-cutting problem of producing envy-freeallocations, restricted to the case of four agents. The problem asks for apartition of the cake to four agents, so that every agent finds her piece atleast as valuable as every other agent's piece. The problem has had aninteresting history so far. Although the case of three agents is solvable withless than 15 queries, for four agents no bounded procedure was known until therecent breakthroughs of Aziz and Mackenzie (STOC 2016, FOCS 2016). The maindrawback of these new algorithms, however, is that they are quite complicatedand with a very high query complexity. With four agents, the number of queriesrequired is close to 600. In this work we provide an improved algorithm forfour agents, which reduces the current complexity by a factor of 3.4. Ouralgorithm builds on the approach of Aziz and Mackenzie (STOC 2016) byincorporating new insights and simplifying several steps. Overall, this yieldsan easier to grasp procedure with lower complexity.

An Improved Envy-Free Cake Cutting Protocol for Four Agents