On Connected Strongly-Proportional Cake-Cutting
CoRR(2023)
摘要
We investigate the problem of fairly dividing a divisible heterogeneous
resource, also known as a cake, among a set of agents. We characterize the
existence of an allocation in which every agent receives a contiguous piece
worth strictly more than their proportional share, also known as a
*strongly-proportional allocation*. The characterization is supplemented with
an algorithm that determines the existence of a connected strongly-proportional
allocation using at most n · 2^n-1 queries. We provide a simpler
characterization for agents with strictly positive valuations, and show that
the number of queries required to determine the existence of a connected
strongly-proportional allocation is in Θ(n^2). Our proofs are
constructive and yield a connected strongly-proportional allocation, when it
exists, using a similar number of queries.
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