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In the example cake, a UM division would give the entire chocolate to Alice and the entire vanilla to George, achieving a utilitarian value of 9 + 4 = 13. This process is easy to carry out when the value functions are piecewise-constant, i.e. the cake can be divided to pieces such that the value density of each piece is constant for all people.
The value measures are accessible only via queries of the form "evaluate a given piece of cake" or "mark a piece of cake with a given value". With n = 2 {\displaystyle n=2} agents, an envy-free division can be found using two queries, via divide and choose .
So, it must be possible to divide the maximum number U−1 of elements into two legal nodes. If this number is odd, then U =2 L and one of the new nodes contains ( U −2)/2 = L −1 elements, and hence is a legal node, and the other contains one more element, and hence it is legal too.
MongoDB, Inc. is an American software company that develops and provides commercial support for the source-available database engine MongoDB, a NoSQL database that stores data in JSON-like documents with flexible schemas.
The definition of proportional division in chore-cutting is the mirror-image of its definition in cake-cutting: each partner should receive a piece that is worth, according to his own personal disutility function, at most / of the total value (where is the total number of partners):
And the numbers speak for themselves: Nvidia: if you invested $1,000 when we doubled down in 2009, you’d have $369,349 !* Apple: if you invested $1,000 when we doubled down in 2008, you’d have ...
One happy beagle is bundling up and spending a warm and cozy Christmas with his new family this holiday season. Meet Copper, an 8-year-old beagle who was recently adopted by PETA staffers ...
In order to calculate the average and standard deviation from aggregate data, it is necessary to have available for each group: the total of values (Σx i = SUM(x)), the number of values (N=COUNT(x)) and the total of squares of the values (Σx i 2 =SUM(x 2)) of each groups.