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Road Coloring Problem Solved
ArieKremen writes "Israeli Avraham Trakhtman, a Russian immigrant mathematician who had been employed as a night watchman, has solved the Road Coloring problem. First posed in 1970 by Benjamin Weiss and Roy Adler, the problem posits that given a finite number of roads, one should be able to draw a map, coded in various colors, that leads to a certain destination regardless of the point of origin. The 63-year-old Trakhtman jotted down the solution in pencil in 8 pages. The problem has real-world implementation in message and traffic routing."
The guy is actually a mathematician who had to work as a security guard right after he immigrated to Israel, which is common for most immigrants. This guy had lots of formal training solving equations like this.
How soon can we see this implemented in my Garman GPS unit or Google Maps?
Life is not for the lazy.
No, today's XKCD is about the traveling salesman problem. They are very different.
Unfortunately for him, a cheap, safe, mass-market flying car was announced an hour later.
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Since the one in the write-up is borken. Here it is.
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He's in Israel, not the US, dude. Save your diatribe for another time.
from Wikipedia: In the real world, this phenomenon would be as if you called a friend to ask for directions to his house, and he gave you a set of directions that worked no matter where you started from. http://en.wikipedia.org/wiki/Road_Coloring_Conjecture/
Apart from the referenced paper being some months old, the author has an extended paper with an efficient algorithm. See A Subquadratic Algorithm for Road Coloring.
1. Here's wtf the problem even is, for those of us who aren't all up in the "mathematical curiosities" business. Basically the question is, for a specific kind of graph (where you can go from point A to a finite number of points B, C, or D, etc) can you label the possible paths from each point so that, starting from anywhere, you can follow an invariable rule that will get you to a specific destination point. (Check the link, the picture makes much more sense).
2. Apparently his proof was published last September. It's "news" because it's just now hitting the semi-mainstream press. You people fail at nerddom.
Freedom isn't free; its price is the well-being of others.
"Some people think they need to be complicated. I think they need to be nice and simple."
The man is a True Genius. Insight to all of out out there, that is the proper way of thinking.
Do not look at laser with remaining good eye.
Actually, if he were to put it on a SD card, it'd take up less than 1 square inch...
Where's my PEDANTIC:-1 option?
- Despite popular opinion, I am not perfect.
In Soviet Russia they say that because Americans were so poor mathematicians, they had to invent the computer...
The Wise adapts himself to the world. The Fool adapts the world to himself. Therefore, all progress depends on the Fool.
If you RTFA (yes, I must be new here) he worked as a night watchman when he first moved to Isreal. He's been working in mathematics for over a decade.
Originally from Yekaterinburg, Russia, Trahtman was an accomplished mathematician when he came to Israel in 1992, at age 48. But like many immigrants in the wave that followed the breakup of the Soviet Union, he struggled to find work in the Jewish state and was forced into stints working maintenance and security before landing a teaching position at Bar Ilan in 1995.
You might as well say the 2002 Nobel prize in economics went to a lieutenant in the army. It's just a minor detail that he was a lieutenant 50 years before winning the prize.
Forty-two.
Justice is the sheep getting arrested while an impartial judge declares the vote void.
The question behind road coloring is this: Given a directed network with out-degree 2 (from any place you can get to exactly two other places), we want to color the edges leading out of each node red or blue so the following "universal directions" condition exists: For any final destination A, there is a set of directions (e.g. take red three times, then blue twice, then red again) that gets you to A no matter where you started from. It may not be the shortest path, but you'll get there. There is one obvious obstruction and one slightly less obvious obstruction: If your network is disconnected so you can't get to A from your starting point no matter what path you follow, you're clearly stuck. On the other hand, there's also a "periodicity" obstruction if all of the cycles of the graph are multiples of the same number. For example, suppose that you were trying to give universal directions for a square, where the roads in question connected every vertex to its two neighbors. If I want to go from my starting point to an adjacent vertex, I have to take an odd number of steps. If I want to go from my starting point to the opposite vertex, I have to take an even number of steps. This means I can't even know how many steps I have to take (let along which steps) unless I knew where I started. It was conjectured, and Trahtman showed, that these two are the only possible obstructions. In particular, he even gives an algorithm for figuring out how to label the roads quickly. I guess the applications I'd see in this are for algorithms and the design of autonomous systems. The idea here is that, if the robot gets stuck somewhere in a multi-step procedure, you may want it to restart from the beginning. However, this can be difficult if the robot does not know where it is in the procedure, or even where it is physically. Trahtman's algorithm could allow you to exchange some computation at the beginning of the procedure (which can be done before the robot goes out, for example), for this "reset" functionality. I don't know whether this is feasible or not though.
Proof at last, that that guy who kept saying, "You can't get there from here" is a bloody liar.
Mir tut es leid, Menschen daß Einfältigfehlersuchenbaumfolgendenaffen sind.