Probabilistic Bidding Gives Optimal Distributed Resource Allocation

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Probabilistic Bidding Gives Optimal Distributed Resource Allocation
John Reif
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This can be done in constant (3 steps) parallel time by using the concurrent read-e;tciu3ive write model and a summation binary tree of depth 3. M IS used to count winners during the monitoring period.
Each user i uses also a shared (for all its parallel subprocesses) variable L^ . It allows concurrent reads and concurrent writes of the same value. L^ is used to identify situations in which all wanted resources have been proposed to be allocated to user i, at the same time.
The counters counter
..., counter. Count steps of respectively i, 3 in a round. Note also that every time a user (or resource allocator) p (1) modifies a flag and then (2) reads a flag of a resource allocator (or user) q to see its answer, we allow for \^ - (r„, yr^^ r, ' " ■^ ^^^^^ between the two actions of p (these steps allow tor at least 2 steps of process q so that q can read the asking flag and answer bacX) .
We now present formally the rounds of a user i and a resource allocator j. Note that, in the code which follows, the section of code between cobegin, and coend is executed (in a synchronous fashion) by all the parallel subprocesses of the process to which the cobegin-coend bloc)c belongs.


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