Hash tables can be much faster


"It pertains to a related, though slightly different, situation: In 1985, Yao looked not only at the worst-case times for queries, but also at the average time taken across all possible queries. He proved that hash tables with certain properties —including those that are labeled greedy, which means that new elements must be placed in the first available spot —could never achieve an average time better than log x.

"Farach-Colton, Krapivin and Kuszmaul wanted to see if that same limit also applied to non-greedy hash tables. They showed that it did not by providing a counterexample, a non-greedy hash table with an average query time that’s much, much better than log x. In fact, it doesn’t depend on x at all. 

"'You get a number,' Farach-Colton said, 'something that is just a constant and doesn’t depend on how full the hash table is.'
 
"The fact that you can achieve a constant average query time, regardless of the hash table’s fullness, was wholly unexpected —even to the authors themselves.

"The team’s results may not lead to any immediate applications, but that’s not all that matters, [Alex] Conway said. 'It’s important to understand these kinds of data structures better. You don’t know when a result like this will unlock something that lets you do better in practice'."



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