Close Menu
Technology Mag

    Subscribe to Updates

    Get the latest creative news from FooBar about art, design and business.

    What's Hot

    Meet Soham Parekh, the engineer burning through tech by working at three to four startups simultaneously

    July 3, 2025

    Identities of More Than 80 Americans Stolen for North Korean IT Worker Scams

    July 3, 2025

    Here are the letters that convinced Google and Apple to keep TikTok online

    July 3, 2025
    Facebook X (Twitter) Instagram
    Subscribe
    Technology Mag
    Facebook X (Twitter) Instagram YouTube
    • Home
    • News
    • Business
    • Games
    • Gear
    • Reviews
    • Science
    • Security
    • Trending
    • Press Release
    Technology Mag
    Home » This New Algorithm for Sorting Books or Files Is Close to Perfection
    Science

    This New Algorithm for Sorting Books or Files Is Close to Perfection

    News RoomBy News RoomFebruary 19, 20254 Mins Read
    Facebook Twitter Pinterest LinkedIn Reddit WhatsApp Email

    The original version of this story appeared in Quanta Magazine.

    Computer scientists often deal with abstract problems that are hard to comprehend, but an exciting new algorithm matters to anyone who owns books and at least one shelf. The algorithm addresses something called the library sorting problem (more formally, the “list labeling” problem). The challenge is to devise a strategy for organizing books in some kind of sorted order—alphabetically, for instance—that minimizes how long it takes to place a new book on the shelf.

    Imagine, for example, that you keep your books clumped together, leaving empty space on the far right of the shelf. Then, if you add a book by Isabel Allende to your collection, you might have to move every book on the shelf to make room for it. That would be a time-consuming operation. And if you then get a book by Douglas Adams, you’ll have to do it all over again. A better arrangement would leave unoccupied spaces distributed throughout the shelf—but how, exactly, should they be distributed?

    This problem was introduced in a 1981 paper, and it goes beyond simply providing librarians with organizational guidance. That’s because the problem also applies to the arrangement of files on hard drives and in databases, where the items to be arranged could number in the billions. An inefficient system means significant wait times and major computational expense. Researchers have invented some efficient methods for storing items, but they’ve long wanted to determine the best possible way.

    Last year, in a study that was presented at the Foundations of Computer Science conference in Chicago, a team of seven researchers described a way to organize items that comes tantalizingly close to the theoretical ideal. The new approach combines a little knowledge of the bookshelf’s past contents with the surprising power of randomness.

    “It’s a very important problem,” said Seth Pettie, a computer scientist at the University of Michigan, because many of the data structures we rely upon today store information sequentially. He called the new work “extremely inspired [and] easily one of my top three favorite papers of the year.”

    Narrowing Bounds

    So how does one measure a well-sorted bookshelf? A common way is to see how long it takes to insert an individual item. Naturally, that depends on how many items there are in the first place, a value typically denoted by n. In the Isabel Allende example, when all the books have to move to accommodate a new one, the time it takes is proportional to n. The bigger the n, the longer it takes. That makes this an “upper bound” to the problem: It will never take longer than a time proportional to n to add one book to the shelf.

    The authors of the 1981 paper that ushered in this problem wanted to know if it was possible to design an algorithm with an average insertion time much less than n. And indeed, they proved that one could do better. They created an algorithm that was guaranteed to achieve an average insertion time proportional to (log n)2. This algorithm had two properties: It was “deterministic,” meaning that its decisions did not depend on any randomness, and it was also “smooth,” meaning that the books must be spread evenly within subsections of the shelf where insertions (or deletions) are made. The authors left open the question of whether the upper bound could be improved even further. For over four decades, no one managed to do so.

    However, the intervening years did see improvements to the lower bound. While the upper bound specifies the maximum possible time needed to insert a book, the lower bound gives the fastest possible insertion time. To find a definitive solution to a problem, researchers strive to narrow the gap between the upper and lower bounds, ideally until they coincide. When that happens, the algorithm is deemed optimal—inexorably bounded from above and below, leaving no room for further refinement.

    Share. Facebook Twitter Pinterest LinkedIn WhatsApp Reddit Email
    Previous ArticleApple no longer sells new iPhones with Lightning ports
    Next Article Mira Murati Is Ready to Tell the World What She’s Working On

    Related Posts

    A European Startup’s Spacecraft Made It to Orbit. Now It’s Lost at Sea

    July 3, 2025

    The Next Acetaminophen Tablet You Take Could Be Made From PET

    July 2, 2025

    How Much Energy Does AI Use? The People Who Know Aren’t Saying

    July 2, 2025

    Space Elevators Could Totally Work—if Earth Days Were Much Shorter

    July 2, 2025

    Methane Pollution Has Cheap, Effective Solutions That Aren’t Being Used

    July 2, 2025

    How to Make AI Faster and Smarter—With a Little Help From Physics

    July 1, 2025
    Our Picks

    Identities of More Than 80 Americans Stolen for North Korean IT Worker Scams

    July 3, 2025

    Here are the letters that convinced Google and Apple to keep TikTok online

    July 3, 2025

    A Group of Young Cybercriminals Poses the ‘Most Imminent Threat’ of Cyberattacks Right Now

    July 3, 2025

    Apple’s colorful Watch Solo Loop bands are up to 70 percent off now

    July 3, 2025
    • Facebook
    • Twitter
    • Pinterest
    • Instagram
    • YouTube
    • Vimeo
    Don't Miss
    Security

    How to Protest Safely in the Age of Surveillance

    By News RoomJuly 3, 2025

    If you insist on using biometric unlocking methods to have faster access to your devices,…

    E Ink is turning the laptop touchpad into an e-reader for AI apps

    July 3, 2025

    US Supreme Court Upholds Texas Porn ID Law

    July 3, 2025

    A European Startup’s Spacecraft Made It to Orbit. Now It’s Lost at Sea

    July 3, 2025
    Facebook X (Twitter) Instagram Pinterest
    • Privacy Policy
    • Terms of use
    • Advertise
    • Contact
    © 2025 Technology Mag. All Rights Reserved.

    Type above and press Enter to search. Press Esc to cancel.