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

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Computer scientists often deal with abstract problems that are hard to understand, but the book and at least one shelf owner an exciting new algorithm is important to anyone. The algorithm library adds the problem (more formally, “list labeling” problems). The challenge is the somehow sorted order – for example, creating a strategy to organize books that reduce how long it takes to place a new book on the shelf.

For example, imagine that you keep your books clamped together, leaving the empty space on the right of the shelf. Then, if you add a book from Isabel Alam to your collection, you may have to transfer each book on the shelf to create a place for it. This will be a time -related operation. And if you get a book in Douglas Adams you need to do it again. The better system will leave the uninterrupted space delivered across the shelf – but how, exactly how to distribute them?

This problem was introduced in one 1981 paperAnd it is just beyond the provision of librarians with organizational directions. Because the problem also applies to the format of the hard drive and database in the database, where the items will be sorted may be the number of billion. The meaning of an inefficient system is significant waiting time and the main calculation. Researchers have invented some skilled methods to save items, but they wanted to determine the best possible way for a long time.

Last year, in A study It was presented at the Foundations of the Computer Science Conference in Chicago, a group of seven researchers described a way to organize items close to theoretical ideals. The new method of the bookstore of the new method randomly combines the little knowledge of the past contents with amazing energy.

“This is a very important problem,” SheetA computer scientist at the University of Michigan, because today we rely on many data structures, storing data in order. He says “highly inspired” the new job [and] One of the best three favorite papers of the year is one of the best. “

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So how does a good-formed bookstore measure? A common way is to see how long it takes to insert a separate item. Naturally, it depends on how many items are in the first place, it is usually a value marked by NThe In the examples of Isabel Alende, when all the books have to move to a new one, it takes the time it takes proportion to NThe Large NIt takes as long as it takes. It makes it a “upper bound” of the problem: it doesn’t take longer than proportion N To add a book to the shelves.

The authors of the paper of 1981 initialized the problem they wanted to know if the average insert was possible to design any algorithm over time NThe And in fact, they have proven that someone can do better. They have created an algorithm that is proportional to the average insert (guaranteed to the log achievement N)²The This algorithm had two features: it was “deterministic” which means its decisions depend on any randomity, and it was “smooth” and the books must be equally spread between the shelf subsections where the insert (or deleted) is made Are. The authors opened this question whether the above limit could be further improved. For more than four decades, no one has been able to do so.

However, the intermediate years have seen the improvement of the bounds below. When the upper limit specifies the maximum possible time required to insert a book, the lower limit gives the fastest insert time. To find a specific solution to a problem, researchers ideally try to narrow the interval between the upper and lower limits until they match them. The algorithm is considered the best when it happens – bound up and down from the top and bottom, leaving no place for more refinement.