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A piecewise-constant valuation is a kind of a function that represents the utility of an agent over a continuous resource, such as land. It occurs when the resource can be partitioned into a finite number of regions, and in each region, the value-density of the agent is constant. A piecewise-uniform valuation is a piecewise-constant valuation in which the constant is the same in all regions.
Piecewise-constant and piecewise-uniform valuations are particularly useful in algorithms for fair cake-cutting.
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