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Scientists Find Optimal Balance of Data Storage and Time

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Researchers have spent decades building hash tables that attempt to maximize speed and minimize memory.

Hash tables are a major class of data structures that offer an especially convenient method for accessing and altering information in massive databases.

Credit: Allison Li/Quanta Magazine

About 70 years ago, an engineer at IBM named Hans Peter Luhn quietly changed the course of computer science. Luhn already held several patents, including one for a device that could measure a cloth's thread count and another for a guide that determined what mixed drinks you could make from the ingredients in your kitchen. But in a 1953 internal IBM paper, he proposed a new technique for storing and retrieving information that is now built into just about all computational systems: the hash table.

Hash tables are a major class of data structures. They offer an especially convenient method for accessing and altering information in massive databases. But this technology comes with an unavoidable trade-off.

In a 1957 paper published in the IBM Journal of Research and Development, W. Wesley Peterson identified the main technical challenge that hash tables pose: They need to be fast, meaning that they can quickly retrieve the necessary information. But they also need to be compact, using as little memory as possible. These twin objectives are fundamentally at odds. Accessing and modifying a database can be done more quickly when the hash table has more memory; and operations become slower in hash tables that use less space. Ever since Peterson laid out this challenge, researchers have tried to find the best balance between time and space.

Computer scientists have now mathematically proved that they have found the optimal trade-off. The solution came from a pair of recent papers that complemented each other. "These papers resolve the long-standing open question about the best possible space-time trade-offs, yielding deeply surprising results that I expect will have a significant impact for many years to come," said Michael Mitzenmacher, a computer scientist at Harvard University who was not involved in either study.

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