Original version From This story Appeared in Quanta Magazine.
Computer scientists often deal with abstract problems that are difficult to understand, but an exciting new algorithm is important to anyone who owns a book and at least one shelf. This algorithm is what the problem of sorting the library (formally, the “label list”). The challenge is that a strategy for organizing books is somehow sorted – for example, for example – to minimize the time required to put a new book on the shelf.
Imagine, for example, that you are collecting your books and putting the empty space on the right side of the shelf. Then, if you add a book by Isabel Allende to your collection, you may have to move each book on the shelf to create a place. This will be a time -consuming action. And if you later get a book from Douglas Adams, you have to do it again. A better arrangement will distribute unused spaces throughout the shelf – but how exactly should be distributed?
This problem was introduced in a 1981 article and is beyond providing organizational guidance to librarians. The reason is that this problem also applies to the order of files on hard drives and databases, where things that need to be arranged can be numbered in billions. An inefficient system means a significant waiting time and a major computational cost. Researchers have invented some efficient ways to store items, but they have long been trying to determine the best possible way.
Last year, in a study presented at the Conference on Computer Science Foundations in Chicago, a team of seven researchers described a way to organize things that amazingly close to ideal theoretical. The new approach of knowledge combines a little knowledge of past material with random surprise power.
“This is a very important problem,” said Set Petty, a computer scientist at the University of Michigan. He called the new work “very inspiring” [and] Easily one of my top three interesting articles of the year. “
Narrow boundaries
So how to measure a good arranged book shelf? One common method is to see how long it takes to enter a separate item. Naturally, it depends on the fact that in the first place there is the number of cases, the amount that is usually specified by LetterHuman beings in Isabel Alland, when all books have to move to accommodate a new one, time is required to fit it LetterHuman beings LetterThe longer it takes. This makes this issue a “upper limit” to the problem: it never takes more than one time appropriate to it Letter To add a book to the shelf.
The authors of the 1981 article raised in this problem wanted to know if the algorithm can be designed with a much less inserted time. LetterHuman beings, and in fact, they proved that one can do better. They created an algorithm that is guaranteed to achieve a moderate insertion of (login entry Letter)2Human algorithm had two characteristics: “definitive”, meaning that its decisions did not depend on any accident, as well as “smooth”, meaning that books should be played evenly under the shelf sections. It is inserted (or deleted). The authors have opened the question whether the upper boundary can be even improved. For more than four decades, no one could do it.
However, years of intervention have witnessed progress at low border. While the upper part specifies the maximum possible time to enter a book, the low range of the fastest possible time gives. To find a definite solution to a problem, the researchers are trying to limit the gap between the upper and lower bounds, ideally until they coincide. When this happens, the algorithm is considered to be optimized – illegally limited from the top and bottom and no room for refinement remains.
