Abstract
In the cake cutting problem, one allocates a heterogeneous divisible resource (cake) to n participating agents. The central criteria of an allocation to satisfy and optimize is envy-freeness and efficiency. In this paper, we consider cake cutting with single-peaked preferences: each agent is assumed to have a favorite point in the cake; the further a piece of cake is from her favorite point, the less her valuation on this piece is. Under this assumption, agents can be considered as a point embedded in a metric space, and thus this setting models many practical scenarios. We present a protocol in the standard query model which outputs an envy-free allocation in linear running time.
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Acknowledgements
The authors thank Xiaodong Hu, Xujin Chen, and Minming Li for support and suggestions. They also thank all the reviewers of COCOA 2019 for comments.
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Wang, C., Wu, X. (2019). Cake Cutting with Single-Peaked Valuations. In: Li, Y., Cardei, M., Huang, Y. (eds) Combinatorial Optimization and Applications. COCOA 2019. Lecture Notes in Computer Science(), vol 11949. Springer, Cham. https://doi.org/10.1007/978-3-030-36412-0_41
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DOI: https://doi.org/10.1007/978-3-030-36412-0_41
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