Optimal Proportional Cake Cutting with Connected Pieces

We consider the classic cake cutting problem where one allocates a divisible to n participating agents. Among all valid divisions, fairness and efficiency (a.k.a. ~social welfare) are most critical criteria satisfy optimize, respectively. study computational complexity of computing an optimal division given conditions that allocation satisfies proportional assigns each agent connected piece. For linear valuation functions, we give polynomial time approximation scheme compute allocation. On other hand, show is NP-hard approximate within factor Ω 1/√n for general piecewise constant normalized functions.