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How I Solved Sparse Rulers
Ed Pegg
In a sparse ruler, such as {0, 1, 6, 9, 11, 13}, all the distances can still be measured even though many marks are missing. The speaker has proven, by construction, that sparse rulers of any length L can be constructed with no more than round (sqrt(3 L + 9/4)) + 1 marks. In addition, on a single laptop, Mathematica was used to find more solutions than a large Intel supercluster. Searching methods, sparse rulers, Golomb rulers and related objects will be discussed, and then some unsolved problems will be discussed.
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