That classic result was a way to transform any algorithm with a given time budget into a new algorithm with a slightly smaller space budget. Williams saw that a simulation based on squishy pebbles would make the new algorithm’s space usage much smaller—roughly equal to the square root of the original algorithm’s time budget. That new space-efficient algorithm would also be much slower, so the simulation was not likely to have practical applications. But from a theoretical point of view, it was nothing short of revolutionary.
For 50 years,…
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