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Approximating Euler Paths

When an Euler path is impossible, we can get an approximate path In the approximate path, some edges will need to be retraced An optimal approximation of a Euler path is a path with the minimum number of edge retraces. Approximating Euler Paths.

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Approximating Euler Paths

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  1. When an Euler path is impossible, we can get an approximate path • In the approximate path, some edges will need to be retraced • An optimal approximation of a Euler path is a path with the minimum number of edge retraces Approximating Euler Paths

  2. Graphs (or shapes) with repeated paterns can be defined parametrically (in terms of a parameter, say k) • We define a D-k Graph (Diamond-k Graph, where k  0) Defining Graphs using Parameters

  3. D-0 Graph

  4. D-1 Graph

  5. D-2 Graph

  6. Draw the graphs: • D-3 • D-4 • D-5 • Take home question: What is the minimum number of edge retraces in an optimal approximation of a Euler path in a D-5 graph? Higher-order D graphs

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