Approximation Algorithms for Envy-Free Cake Division with Connected Pieces

Barman, S and Kulkarni, P (2023) Approximation Algorithms for Envy-Free Cake Division with Connected Pieces. In: 50th International Colloquium on Automata, Languages, and Programming, ICALP 2023, 10 - 14 July 2023, Paderborn.

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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 (41 + o(1))-additively envy-free and (12 − 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.

Item Type:	Conference Paper
Publication:	Leibniz International Proceedings in Informatics, LIPIcs
Publisher:	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Additional Information:	The copyright for this article belongs to the Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing.
Keywords:	Envy-Cycle Elimination; Envy-Freeness; Fair Division
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	29 Nov 2023 09:32
Last Modified:	29 Nov 2023 09:32
URI:	https://eprints.iisc.ac.in/id/eprint/82911

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