In this case, it means inserting items into a PriorityQueue that contains n items (where n is large - these scalings are only really relevant for big numbers) scales with log(n). Let's say that you've got a queue with 10,000 entries, and it's taking four seconds to insert items (in the worst case). Then you'd expect a queue with 100,000 entries to take five second to insert items [because log(10000) = 4 and log(100000) = 5].
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