As of January 2020, Papadimitreo has been thinking about the principle of pigeon hole for 30 years. So he was surprised when a lively conversation with his partner repeatedly attracted him to a simple twist on the principle he never considered: What would happen if there were less pigeons than holes? In this case, any arrangement of pigeons should leave some empty holes. Again, this seems clear. But does the pigeon’s principle change have any interesting consequences?
It seems as if this “empty Pijon Hole” principle is just by another name. But this is not, and its completely different roles have made it a new and fruitful source to classify computation issues.
To understand the empty Pajon Hole principle, let’s go back as a bank card, which has been transferred to a concert hall with 3,000 seats from the football stadium, which has a small number of possible four -digit pins. The empty Pajon Hole principle commands that some potential pins are not represented at all. If you want to find any of these lost pins, however, it seems that everyone has no better way than just their pin. So far, the empty Pajon Hole Rule is exactly like its more famous counterpart.
The difference is the problem of examining the solution. Imagine that someone says they have found two specific people in the football stadium who have the same pin. In this case, according to the original pigeon hole scenario, there is an easy way to confirm this claim: just ask the two people who are undergoing. But in the case of a concert hall, imagine someone claimed that no one has a 5926 pin. Here, it is impossible to confirm without asking what they have in the audience. This makes the empty pajoon hole principle more disturbed by the ideas of complexity.
Two months after Papadimatrio began to think about the empty Pijon Hole principle, he presented it in a conversation with a potential graduate student. He clearly remembers it, as it came to someone’s last personal conversation with someone before the Covade 19 lockdown. In the next months the house was harmonized, he fought the boat with the implications of the problem of complexity. Finally he and his colleagues published a Paper Regarding search issues that guarantee the empty pajoon hole principle guarantee the solution. He was particularly interested in issues where pigeons holes are in large quantities – ie, where they are much more than pigeons. Keeping the tradition of Uncontrolled abbreviations In the theory of complexity, he termed the problems of this class as APP, for the “abundant multi-faceted empty-pigment hole principle”.
An anxiety in this class was influenced by a famous person 70 -year -old old evidence By the advanced computer scientist Claude Shannon. Shannon proved that solving most computational problems should be naturally difficult, using the argument that relies on the empty Pajon Hole principle (though he did not say it). Still, for decades, computer scientists tried and failed to prove that specific problems are really difficult. Like the disappearance of bank cards, it is important to face difficult problems, even if we cannot identify them.
Historically, researchers have not thought about the process of searching for difficult issues as a search problem that can be analyzed according to mathematics. The point of view of Papadimatrio, which groups this process with other search issues associated with the empty Pajon Hole principle, was featured in its self -reference to taste. Very recent work In the complex theory – it offered a new way to argue the difficulty in proving computational difficulty.
