Contiguous Cake Cutting: Hardness Results and Approximation Algorithms

11/13/2019
by   Paul W. Goldberg, et al.
0

We study the fair allocation of a cake, which serves as a metaphor for a divisible resource, under the requirement that each agent should receive a contiguous piece of the cake. While it is known that no finite envy-free algorithm exists in this setting, we exhibit efficient algorithms that produce allocations with low envy among the agents. We then establish NP-hardness results for various decision problems on the existence of envy-free allocations, such as when we fix the ordering of the agents or constrain the positions of certain cuts. In addition, we consider a discretized setting where indivisible items lie on a line and show a number of hardness results strengthening those from prior work.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/18/2022

Approximation Algorithms for Envy-Free Cake Division with Connected Pieces

Cake cutting is a classic model for studying fair division of a heteroge...
research
06/26/2020

Cutting Polygons into Small Pieces with Chords: Laser-Based Localization

Motivated by indoor localization by tripwire lasers, we study the proble...
research
04/23/2023

Approximate Envy-Freeness in Graphical Cake Cutting

We study the problem of fairly allocating a divisible resource in the fo...
research
04/12/2020

Closing Gaps in Asymptotic Fair Division

We study a resource allocation setting where m discrete items are to be ...
research
05/23/2022

Competitive Equilibrium with Chores: Combinatorial Algorithm and Hardness

We study the computational complexity of finding a competitive equilibri...
research
07/01/2018

An Improved Envy-Free Cake Cutting Protocol for Four Agents

We consider the classic cake-cutting problem of producing envy-free allo...
research
04/28/2020

Fair Division of Time: Multi-layered Cake Cutting

We initiate the study of multi-layered cake cutting with the goal of fai...

Please sign up or login with your details

Forgot password? Click here to reset