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To attain fairness, the allocation is randomized: for each (person, object) pair, a probability is calculated, such that the sum of probabilities for each person and for each object is 1. The probabilistic-serial procedure can compute the probabilities such that each agent, looking at the matrix of probabilities, prefers his row of ...
Random priority (RP), [1] also called Random serial dictatorship (RSD), [2] is a procedure for fair random assignment - dividing indivisible items fairly among people. Suppose partners have to divide (or fewer) different items among them. Since the items are indivisible, some partners will necessarily get the less-preferred items (or no items ...
When all agents have the same additive valuation. Then, every allocation is envy-freeable. An allocation that requires at most (n-1)V subsidy can be found in polynomial time. An allocation minimizes the subsidy iff it minimizes the maximum utility to any agent. Computing such an allocation is NP-hard, and can be solved by the max-product algorithm.
A 1/2-approximate EFx allocation (that also satisfies a different approximate-fairness notion called Maximin Aware) can be found in polynomial time. [20] A 0.618-approximate EFx allocation (that is also EF1 and approximates other fairness notions called groupwise maximin share and pairwise maximin share) can be found in polynomial time. [21]
Fair random assignment (also called probabilistic one-sided matching) is a kind of a fair division problem.. In an assignment problem (also called house-allocation problem or one-sided matching), there are m objects and they have to be allocated among n agents, such that each agent receives at most one object.
A powerful balls-into-bins paradigm is the "power of two random choices [2]" where each ball chooses two (or more) random bins and is placed in the lesser-loaded bin. This paradigm has found wide practical applications in shared-memory emulations, efficient hashing schemes, randomized load balancing of tasks on servers, and routing of packets ...
Blum Blum Shub takes the form + =, where M = pq is the product of two large primes p and q.At each step of the algorithm, some output is derived from x n+1; the output is commonly either the bit parity of x n+1 or one or more of the least significant bits of x n+1.
This guarantees that, for each agent, the bang-for-buck of all objects in his bundle is exactly 1, and the bang-for-buck of all objects in other bundles is at most 1. Hence the allocation is MBB, hence it is also fPO. If the allocation is 3e-pEF1, return it; otherwise proceed to Phase 2. Phase 2: Remove price-envy within MBB hierarchy: