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| Content Provider | ACM Digital Library |
|---|---|
| Author | Edmonds, Jeff Pruhs, Kirk |
| Copyright Year | 2011 |
| Abstract | We consider the well-known cake cutting problem in which a protocol wants to divide a cake among $\textit{n}$ ≥ 2 players in such a way that each player believes that they got a fair share. The standard Robertson-Webb model allows the protocol to make two types of queries, Evaluation and Cut, to the players. A deterministic divide-and-conquer protocol with complexity $\textit{O}(\textit{n}$ log $\textit{n})$ is known. We provide the first a $Ω(\textit{n}$ log $\textit{n})$ lower bound on the complexity of any deterministic protocol in the standard model. This improves previous lower bounds, in that the protocol is allowed to assign to a player a piece that is a union of intervals and only guarantee approximate fairness. We accomplish this by lower bounding the complexity to find, for a single player, a piece of cake that is both rich in value, and thin in width. We then introduce a version of cake cutting in which the players are able to cut with only finite precision. In this case, we can extend the $Ω(\textit{n}$ log $\textit{n})$ lower bound to include randomized protocols. |
| Starting Page | 1 |
| Ending Page | 12 |
| Page Count | 12 |
| File Format | |
| ISSN | 15496325 |
| e-ISSN | 15496333 |
| DOI | 10.1145/2000807.2000819 |
| Volume Number | 7 |
| Issue Number | 4 |
| Journal | ACM Transactions on Algorithms (TALG) |
| Language | English |
| Publisher | Association for Computing Machinery (ACM) |
| Publisher Date | 2011-09-28 |
| Publisher Place | New York |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Cake cutting Fair division |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
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