A guide to experimental algorithmics by Catherine C. McGeoch

By Catherine C. McGeoch

"Computational experiments on algorithms can complement theoretical research by means of displaying what algorithms, implementations, and speed-up equipment paintings most sensible for particular machines or difficulties. This booklet publications the reader in the course of the nuts and bolts of the main experimental questions: What should still I degree? What inputs may still I try? How do I learn the knowledge? Answering those questions wishes rules from set of rules design Read more...

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If measurements do not change with n, C(n) is constant. 2. If costs increment by a constant as n doubles, for example, if C(n) = 33, 37, 41, 45, then C(n) ∈ (log n). 3. If costs double as n doubles, C(n) is linear. 4. To determine whether C(n) ∈ (n log n), divide each measurement by n and check whether the result C(n)/n increments by a constant. 5. If cost quadruples each time n doubles, C(n) ∈ (n2 ). Similar rules can be worked out for other common function classes; see Sedgewick [22] for details.

The color count achieved by Greedy depends on the order in which vertices are considered. For example, if vertices are colored in reverse order 8 . . 1, the color count would be 3: 8 7 6 Red Yellow Yellow 5 Green 4 Red 3 2 Red Yellow 1 Green There must exist a vertex order for which Greedy finds an optimal coloring, but since there are n! vertex orders, trying them all takes too much time. 3 applies Greedy I times, using a random vertex permutation each time, and remembers the best coloring it finds.

But they may fail to answer what may be the main question: how well does the algorithm perform in practice? Inputs from real-world applications are ideal for answering that question, but, on the other hand, they can be hard to find in sufficient quantities for testing. Also they may contain highly problem-specific hidden structures that produce hard-to-explain and therefore hard-to-generalize results. The choice of instance classes to test should reflect general experimental goals as well as the specific question at hand: • To meet goals of correctness and validity, use stress-test inputs and check that random generators really do generate instances with the intended properties.

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