This new algorithm is close to perfection for sorting books or files

Original version one This story appeared How many magazines.

Computer scientists often deal with abstract problems that are difficult to understand, but are a new algorithm for anyone who owns the book and has at least one shelf. The algorithm reports something called Sorting Problem (officially, the “list label” problem). The call minimizes how long it takes to place a new book on the shelf, for example, a strategy to organize a book with some types of ordered orders.

For example, because you glued your books together, leave your books together, leaving the empty space in the right part of the shelf. Then, if you add ISABEL ALLINDE to your collection, you must move on the shelf to put each book in the room. In this case, it would be a consumer operation. If you then buy a book by Douglas Adams, you need to do it again. A better arrangement leaves empty spaces distributed along the shelf, but how, exactly how should these be distributed?

This problem was presented in one 1981 PaperAnd this is simply going beyond providing librarians with organizational leadership. Because it also applies to files in both hard drives and databases, where the items can be considered here. An inefficient system means significant waiting period and basic calculation costs. Researchers invented some effective methods for keeping items, but they wanted to determine the best possible way.

Last year, in a study This was presented in the foundations of the computer science conference in Chicago, seven researchers described a way to organize items near the theoretical ideal. The new approach combines the past content of the bookshelf with surprisingly surprising power.

“It’s a very important problem,” he said Seth PettieMany of the information structures are consistently trusted in a store information today because of a computer scientist at Michigan University. The new job is one of my best three favorite documents of the year. “

Narrowing

But how does it measure a sorted bookshelf? A common road is to see how much time it takes to enter an individual item. Of course, this depends on a value of how many substances, which are usually marked n. In the example of Isabel AllINDE, when all the books must move to place a new, the needed time is proportional n. How big is it nhow much it takes. This makes this problem “up border”: This will never take longer than a time proportional n to add a book to the shelf.

In this problem, the authors of the 1981 documents in 1981 wanted to know that an algorithm is possible to design an algorithm n. Indeed, they have proven to do something better. They have created an algorithm given to achieve a medium additional time (input) n(^2nd. The two properties of this algorith were: “Deterministic”, the meaning was not randomly “smooth”, and it means that the places (or deletions of books are not equally spreading in places (or deletions). The authors opened the issue of further improvement of the upper border. For more than four decades, no one can do this.

However, the intervention did the years of progress in the lower boundary. Although the top border determines the maximum possible time to enter a book, the low border gives the fastest wear time. To find a definitive solution to a problem, researchers try to narrow the gap between upper and lower boundaries until they overlap. When this happened, the algorithm is lower and below the top and below, and the lower level, did not place a place to improve.