License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2023.16
URN: urn:nbn:de:0030-drops-180685
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18068/
Barman, Siddharth ;
Kulkarni, Pooja
Approximation Algorithms for Envy-Free Cake Division with Connected Pieces
Abstract
Cake cutting is a classic model for studying fair division of a heterogeneous, divisible resource among agents with individual preferences. Addressing cake division under a typical requirement that each agent must receive a connected piece of the cake, we develop approximation algorithms for finding envy-free (fair) cake divisions. In particular, this work improves the state-of-the-art additive approximation bound for this fundamental problem. Our results hold for general cake division instances in which the agents' valuations satisfy basic assumptions and are normalized (to have value 1 for the cake). Furthermore, the developed algorithms execute in polynomial time under the standard Robertson-Webb query model.
Prior work has shown that one can efficiently compute a cake division (with connected pieces) in which the additive envy of any agent is at most 1/3. An efficient algorithm is also known for finding connected cake divisions that are (almost) 1/2-multiplicatively envy-free. Improving the additive approximation guarantee and maintaining the multiplicative one, we develop a polynomial-time algorithm that computes a connected cake division that is both (1/4 +o(1))-additively envy-free and (1/2 - o(1))-multiplicatively envy-free. Our algorithm is based on the ideas of interval growing and envy-cycle elimination.
In addition, we study cake division instances in which the number of distinct valuations across the agents is parametrically bounded. We show that such cake division instances admit a fully polynomial-time approximation scheme for connected envy-free cake division.
BibTeX - Entry
@InProceedings{barman_et_al:LIPIcs.ICALP.2023.16,
author = {Barman, Siddharth and Kulkarni, Pooja},
title = {{Approximation Algorithms for Envy-Free Cake Division with Connected Pieces}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {16:1--16:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2023/18068},
URN = {urn:nbn:de:0030-drops-180685},
doi = {10.4230/LIPIcs.ICALP.2023.16},
annote = {Keywords: Fair Division, Envy-Freeness, Envy-Cycle Elimination}
}
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Keywords: |
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Fair Division, Envy-Freeness, Envy-Cycle Elimination |
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Collection: |
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50th International Colloquium on Automata, Languages, and Programming (ICALP 2023) |
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Issue Date: |
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2023 |
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Date of publication: |
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05.07.2023 |
