Contiguous cake cutting: hardness results and approximation algorithms
We study the fair allocation of a cake, which serves as a metaphor for a divisible resource, under the requirement that each agent should receive a contiguous piece of the cake. While it is known that no finite envy-free algorithm exists in this setting, we exhibit efficient algorithms that produce...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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AI Access Foundation
2020
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| _version_ | 1797058048802422784 |
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| author | Goldberg, PW Hollender, A Suksompong, W |
| author_facet | Goldberg, PW Hollender, A Suksompong, W |
| author_sort | Goldberg, PW |
| collection | OXFORD |
| description | We study the fair allocation of a cake, which serves as a metaphor for a divisible resource, under the requirement that each agent should receive a contiguous piece of the cake. While it is known that no finite envy-free algorithm exists in this setting, we exhibit efficient algorithms that produce allocations with low envy among the agents. We then establish NP-hardness results for various decision problems on the existence of envy-free allocations, such as when we fix the ordering of the agents or constrain the positions of certain cuts. In addition, we consider a discretized setting where indivisible items lie on a line and show a number of hardness results extending and strengthening those from prior work. Finally, we investigate connections between approximate and exact envy-freeness, as well as between continuous and discrete cake cutting. |
| first_indexed | 2024-03-06T19:45:05Z |
| format | Journal article |
| id | oxford-uuid:2201a002-df92-488a-9e26-3649652f74a1 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:45:05Z |
| publishDate | 2020 |
| publisher | AI Access Foundation |
| record_format | dspace |
| spelling | oxford-uuid:2201a002-df92-488a-9e26-3649652f74a12022-03-26T11:36:28ZContiguous cake cutting: hardness results and approximation algorithmsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2201a002-df92-488a-9e26-3649652f74a1EnglishSymplectic ElementsAI Access Foundation2020Goldberg, PWHollender, ASuksompong, WWe study the fair allocation of a cake, which serves as a metaphor for a divisible resource, under the requirement that each agent should receive a contiguous piece of the cake. While it is known that no finite envy-free algorithm exists in this setting, we exhibit efficient algorithms that produce allocations with low envy among the agents. We then establish NP-hardness results for various decision problems on the existence of envy-free allocations, such as when we fix the ordering of the agents or constrain the positions of certain cuts. In addition, we consider a discretized setting where indivisible items lie on a line and show a number of hardness results extending and strengthening those from prior work. Finally, we investigate connections between approximate and exact envy-freeness, as well as between continuous and discrete cake cutting. |
| spellingShingle | Goldberg, PW Hollender, A Suksompong, W Contiguous cake cutting: hardness results and approximation algorithms |
| title | Contiguous cake cutting: hardness results and approximation algorithms |
| title_full | Contiguous cake cutting: hardness results and approximation algorithms |
| title_fullStr | Contiguous cake cutting: hardness results and approximation algorithms |
| title_full_unstemmed | Contiguous cake cutting: hardness results and approximation algorithms |
| title_short | Contiguous cake cutting: hardness results and approximation algorithms |
| title_sort | contiguous cake cutting hardness results and approximation algorithms |
| work_keys_str_mv | AT goldbergpw contiguouscakecuttinghardnessresultsandapproximationalgorithms AT hollendera contiguouscakecuttinghardnessresultsandapproximationalgorithms AT suksompongw contiguouscakecuttinghardnessresultsandapproximationalgorithms |