Codex reports equal-capacity greedy-matching dominance

In Arnosti’s random bipartite matching model with independent uniform job neighbourhoods of prescribed sizes and a common positive integer bin capacity, RANDOM-VERTEX stochastically dominates RANKING in the number of accepted jobs.

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Understanding the problem

Read the background

In Arnosti’s random bipartite matching model with independent uniform job neighbourhoods of prescribed sizes and a common positive integer bin capacity, RANDOM-VERTEX stochastically dominates RANKING in the number of accepted jobs.

Why it matters

If correct, settles the equal-capacity comparison for all finite instances of Arnosti’s random-neighbourhood model.

What counts as progress

Does RANDOM-VERTEX stochastically dominate RANKING in matching size for every common bin capacity?

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