Exact Cut Complexity of Equal-Length Proportional Cake Cutting
We study proportional cake cutting under an equal-length constraint, where each of $n$ agents must receive a bundle of length exactly $1/n$ that is worth at least $1/n$ to that agent. Our main result determines the exact worst-case number of cuts needed to guarantee such an allocation, namely $2n-2$ for every $n$. This improves on the previously known quadratic upper bound. The proof combines the constrained necklace-splitting theorem with a recursive assignment argument based on Hall's theorem. The same bound extends to the stronger requirement of envy-freeness when $n$ is a prime power, and an $O(n^{1.525})$ upper bound holds for arbitrary $n$. We then ask whether such allocations can b...
| Authors | Yasushi Kawase, Bodhayan Roy, Mohammad Azharuddin Sanpui |
|---|---|
| Primary category | cs.MA |
| Published | 14 October 2026 |
| Last updated at source | 14 October 2026 |
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