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Cost-effectiveness of algorithms

Abstract : In this paper we discuss how to assess the performance of algorithms for optimisation problems in a way that balances solution quality and time. We propose measures of cost-effectiveness for such algorithms. These measures give the gain in solution quality per time unit over a sequence of inputs, and give a basis for deciding which algorithm to use when aiming for best accumulated solution quality for a given time investment over such an input sequence. Cost-effectiveness measures can be defined for both average-case and worst-case performance. We apply these ideas to three problems: maximum matching, graph colouring and Kolmogorov complexity. For the latter, we propose a cost-effectiveness measure for the time-bounded complexity Kτ(x), and argue that it can be used to measure the cost-effectiveness both of finding a short program to output x and of generating x from such a program. Under mild assumptions, we show that (roughly speaking) if the time-bounded complexity Kτ(x) is to be a cost-effective approximation to K(x) then τ(n)=O(n2).
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Submitted on : Thursday, September 10, 2015 - 3:17:20 PM
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Graham Farr. Cost-effectiveness of algorithms. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2015, Vol. 17 no. 1 (in progress) (1), pp.201--218. ⟨hal-01196858⟩

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