Fair division with minimal withheld information in social networks

We present a study of a few graph-based problems motivated by fair allocation of resources in a social network. The central role in the paper is played by the following problem: What is the largest number of items we can allocate to the agents in the given social network so that each agent hides at...

Full description

Saved in:
Bibliographic Details
Published inTheoretical computer science Vol. 991; p. 114446
Main Authors Bliznets, Ivan, Bukov, Anton, Sagunov, Danil
Format Journal Article
LanguageEnglish
Published Elsevier B.V 12.04.2024
Subjects
EF1 allocation
Fair division
Fixed-parameter tractable
FPT-algorithm
Fair division
Fixed-parameter tractable
EF1 allocation
FPT-algorithm
Online AccessGet full text

Cover

More Information
Summary:We present a study of a few graph-based problems motivated by fair allocation of resources in a social network. The central role in the paper is played by the following problem: What is the largest number of items we can allocate to the agents in the given social network so that each agent hides at most one item and overall at most k items are hidden, and no one envies its neighbors? We show that the problem admits an XP algorithm and is W[1]-hard parameterized by k. Moreover, within the running time, we can identify agents that should hide its items and can construct an ordering in which agents should pick items into its bundles to get a desired allocation. Besides this problem, we also consider the existence and verification versions of this problem. In the existence problem, we are given a social network, valuations, a budget, and the goal is to find an allocation without envy. In the verification problem, we are additionally given an allocation, and the goal is to determine if the allocation satisfies the required property.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2024.114446