Quanta Magazine: “The library sorting problem is used across computer science for organizing far more than just books. A new solution is less than a page-width away from the theoretical ideal. 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 (opens a new tab), 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 (opens a new tab) 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…”