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The chore division problem was introduced by Martin Gardner in 1978. [1] Chore division is often called fair division of bads, in contrast to the more common problem called "fair division of goods" (an economic bad is the opposite of an economic good). Another name is dirty work problem. The same resource can be either good or bad, depending on ...
NOTE: the following related problems are known to be computationally hard: Calculating the 1-of-MMS of a given agent is NP-hard even if all agents have additive preferences (reduction from partition problem). Deciding whether a given allocation is 1-of-MMS is co-NP complete for agents with additive preferences.
Fair item allocation is a kind of the fair division problem in which the items to divide are discrete rather than continuous. The items have to be divided among several partners who potentially value them differently, and each item has to be given as a whole to a single person. [1]
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
Thought of quotitively, a division problem can be solved by repeatedly subtracting groups of the size of the divisor. [1] For instance, suppose each egg carton fits 12 eggs, and the problem is to find how many cartons are needed to fit 36 eggs in total. Groups of 12 eggs at a time can be separated from the main pile until none are left, 3 groups:
Then, for each subject, a new population of 20 divisions was created using a genetic algorithm. This procedure continued for 15 iterations until a best surviving allocation was found. The results were compared to five provably-fair division algorithms: Sealed Bid Knaster, Adjusted Winner, Adjusted Knaster, Division by Lottery and Descending Demand.
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