Travelling Salesman Problem Thesis

I first heard about the traveling salesman problem a few years ago, and it seemed super daunting to me at the time.To be totally honest, even coming back to it now, it still feels a little bit daunting, and it might seem scary to you, too.In fact, some of the most famous problems in the history of computer science have no specific origin that anyone knows of.

Throughout this series, we’ve been building upon our foundation core of computer science, and returning to some of the same concepts repeatedly in an effort to understand them on a more technical level — but only when we feel fully equipped to do so.The same goes for this look into the the traveling salesman problem.In order to understand why this problem is so notorious, we need to wrap our heads around what it is, how we can solve it, why it is important, and what makes it so hard.Indeed, the Seven Bridge problem was just the beginning, and the traveling salesman problem is a prime example of someone building upon the ideas of those who came before him.The “someone” in this scenario is none other than William Rowan Hamilton, an Irish physicist and mathematician who was inspired by and subsequently continued the research of mathematicians who came before him in order to create a subset of mathematical problems that are directly tied to the traveling salesman problem that we are familiar with today.We’ve got a solid foundation to build upon, just like Hamilton did!Once we’re able to wrap our heads around the fact that the traveling salesman problem is really just a graph traversal problem, we can start getting down to business.Just as as dodecahedron has 20 vertices, we could imagine Hamilton’s game as a map of 20 cities.Using this analogy, our traveling salesman would need to find a way through 20 cities, visiting each city once, and ending up exactly where he started.Hamilton’s game was eventually turned into an actual board game.And, if we think about it, even the icosian game is really just another variation on the traveling salesman problem!

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