Parameterized Complexity of Incomplete Connected Fair Division

Harmender Gahlawat, Meirav Zehavi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Fair division of resources among competing agents is a fundamental problem in computational social choice and economic game theory. It has been intensively studied on various kinds of items (divisible and indivisible) and under various notions of fairness. We focus on Connected Fair Division (CFD), the variant of fair division on graphs, where the resources are modeled as an item graph. Here, each agent has to be assigned a connected subgraph of the item graph, and each item has to be assigned to some agent. We introduce a generalization of CFD, termed Incomplete CFD (ICFD), where exactly p vertices of the item graph should be assigned to the agents. This might be useful, in particular when the allocations are intended to be "economical" as well as fair. We consider four well-known notions of fairness: PROP, EF, EF1, EFX. First, we prove that EF-ICFD, EF1-ICFD, and EFX-ICFD are W[1]-hard parameterized by p plus the number of agents, even for graphs having constant vertex cover number (vcn). In contrast, we present a randomized FPT algorithm for PROP-ICFD parameterized only by p. Additionally, we prove both positive and negative results concerning the kernelization complexity of ICFD under all four fairness notions, parameterized by p, vcn, and the total number of different valuations in the item graph (val).

Original languageEnglish
Title of host publication43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2023
EditorsPatricia Bouyer, Srikanth Srinivasan, Srikanth Srinivasan
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959773041
DOIs
StatePublished - 1 Dec 2023
Event43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2023 - Hyderabad, India
Duration: 18 Dec 202320 Dec 2023

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume284
ISSN (Print)1868-8969

Conference

Conference43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2023
Country/TerritoryIndia
CityHyderabad
Period18/12/2320/12/23

Keywords

  • Connected Fair Allocation
  • Fair Division
  • Fixed parameter tractability
  • Kernelization

ASJC Scopus subject areas

  • Software

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