Worse is better. Is there an example?

Question

Is there a widely-used algorithm that has time complexity worse than that of another known algorithm but it is a better choice in all practical si

Answer 1

This example would be the answer if there were no computers capable of storing these large collections.

Presumably the size of the collection was 641K.

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When working in the technical computing group for BAE SYSTEMS, which looked after structural and aerodynamic code for various aircraft, we had a codebase going back at least 25 years (and a third of the staff had been there that long).

Many of the algorithms were optimised for performance on a 16bit mainframe, rather than for scalability. These optimisations were entirely appropriate for 1970s hardware, but performed poorly on larger datasets on the 32 and 64 bit systems which replaced it. If you're choosing something with worse scalability which works better on the hardware you are currently working on, be aware that this is an optimisation, and it may not apply in the future. At the time those 1970s routines were written, data size we put into them in the 2000s was not practical. Unfortunately, trying to extract a clear algorithm from those codes which then could be implemented to suit modern hardware was not trivial.

Short of boiling the oceans, what counts as 'all practical situations' is often a time dependent variable.

Answer 2

Ok, consider solving the traveling sales man problem. The ONLY perfect solution is to test all possible routes. However that becomes impossible with our hardware and time-limits as N increases. So we have thought of many of heuristics.

Which brings us to the answer of your question. Heuristics (worse) are better than brute-force for NP-complete problems. This describes the situation in which "Worse is Better" is always true.

Answer 3

Coppersmith–Winograd algorithm for square matrix multiplication. Its time complexity is O(n^2.376) vs. O(n³) of a naive multiplication algorithm or vs. O(n^2.807) for Strassen algorithm.

From the wikipedia article:

However, unlike the Strassen algorithm, it is not used in practice because it only provides an advantage for matrices so large that they cannot be processed by modern hardware (Robinson 2005).

Answer 4

Monte Carlo integration is a probabilistic method of calculating definite integrals that has no guarantee of returning the correct answer. Yet, in real-world situations it returns an accurate answer far faster than provably correct methods.

Answer 5

There exists a polynomial time algorithm for determining primality, but in practice, it's always faster to use an exponential time algorithm or to perform enough probabilistic calculations to have sufficient certainty.

Answer 6

When calculating the median of a group of numbers, you can use an algorithm very similar to quicksort. You partition around a number, and all the bigger ones go to one side, and all the smaller ones go the other side. Then you throw away one side and recursively calculate the median of the larger side. This takes O(n^2) in the worst case, but is pretty fast (O(n) with a low constant) in the average case.

You can get guaranteed worst-case O(n) performance, with a constant of about 40. This is called the median of medians algorithm. In practice, you would never use this.