4 problems

In a connected cake with $n$ agents, suppose each agent may receive at most $k$ disconnected pieces, and measure the optimal social welfare as the sum of the agents' values or the…

Let $n$ players have preferences over the connected pieces of the cake $[0,1]$. An envy-free division is a division of the cake into $n$ connected pieces assigned to the players so…

Universal upper-bound conjecture. For every $n$, every set of $n$ value measures, and every entitlement vector $t$, there exists a $t$-proportional allocation with at most $2n-2$ c…

Consider an instance of the cake-cutting problem with $k$ players. For integers $1\leq p,q\leq k$, the theorem gives bounds $\left\lceil \frac{k-p}{p}\right\rceil$ and…