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# How to Paint Your Way out of a Maze

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Many people don't realize that what we now call "algorithm design" actually dates back to the ancient Greeks! Of course, if you think about it, there's always the "Euclidean Algorithm". A more …

Many people don't realize that what we now call "algorithm design" actually dates back to the ancient Greeks! Of course, if you think about it, there's always the "Euclidean Algorithm". A more dubious example might be Theseus's use of a ball of string to solve the "Labyrinth Problem". (Google "Theseus, Labyrinth, string".) Solutions to this problem got a lot less dubious after graph theory was invited, since a graph turns out to be a good way of representing a maze mathematically. We will examine the classical solutions to this problem, and then throw in a twist --- a Twisted Painting Machine that puts restrictions on which paths we can take to explore the maze. Applications to sewing may also appear, depending on the presence of audience interest and string.

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• 1. How to Paint Your Way out of a Maze Prof. Joshua Holden, Rose-Hulman Inst. of Tech. Joint work with Lana Holden How to Paint Your Way out of a Maze – p. 1/3
• 2. Graphs and Digraphs DeﬁnitionA (loop-free) graph is a set of vertices, V , and a set of edges, E, where each edge is an unordered pair of distinct vertices. Deﬁnition A (loop-free) digraph is a set of vertices, V , and a set of edges, E, where each edge is an ordered pair of distinct vertices. (The order is thought of as indicating a “direction”.) How to Paint Your Way out of a Maze – p. 2/3