Optimal Proportional Cake Cutting with Connected Pieces
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چکیده
We consider the classic cake cutting problem where one allocates a divisible cake to n participating agents. Among all valid divisions, fairness and efficiency (a.k.a. social welfare) are the most critical criteria to satisfy and optimize, respectively. We study computational complexity of computing an efficiency optimal division given the conditions that the allocation satisfies proportional fairness and assigns each agent a connected piece. For linear valuation functions, we give a polynomial time approximation scheme to compute an efficiency optimal allocation. On the other hand, we show that the problem is NP-hard to approximate within a factor of Ω (
منابع مشابه
Resource-monotonicity and Population-monotonicity in Connected Cake-cutting
In the classic cake-cutting problem (Steinhaus, 1948), a heterogeneous resource has to be divided among n agents with different valuations in a proportional way — giving each agent a piece with a value of at least 1/n of the total. In many applications, such as dividing a land-estate or a time-interval, it is also important that the pieces are connected. We propose two additional requirements: ...
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تاریخ انتشار 2012