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The Traveling Salesman Problem answers the question “Given a list of cities you want to visit, what’s the shortest possible distance to visit all of them and return to your starting point? The problem was first described in an 1832 traveling salesman’s manual and has since gone on to stump generations of mathematicians and computer scientists. You might be able to solve the problem for a relatively short route, like 3 cities, but the more cities you add, the more possible routes you have to check. For example, Gharan and colleagues (2011) developed an algorithm that works about 40% of the time.
The “regular” Traveling Salesman Problem involves visiting all vertices on a weighted graph, while an Asymmetrical Traveling Salesman Problem (ATSP) allows for a directed graph.
Asymmetric TSP allows for distances between nodes to be unequal.
Often, optimal routes were laid out to guide the salesman from city to city without wasting energy or time.
The origin of the name“I don’t know who coined the peppier name ‘Traveling Salesman Problem’ for Whitney’s problem, but that name certainly has caught on, and the problem has turned out to be of very fundamental importance.” This computer-generated image of Mona Lisa was created by Robert Bosch as a 100,000 city TSP problem.
The TSP problem is what mathematicians call NP-hard.
Végh published this solution, which works for asymmetrical traveling salesman problems by finding smaller and smaller optimal groups.
The process wasn’t NP-Hard, but it was frustratingly difficult to create at first. Proceeding FOCS ’11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science. “Traveling Salesman Tours.” §5.3.5 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. The Princeton Mathematics Community in the 1930s, Transcript Number 11.
First, there was the problem of all the tones needed to create a black and white image.
I’m going to give credit to Noli Novak and her beautiful stipple portraits for this one.
I spent many hours studying her work and then translating it into a continuous line instead of a series of dots.