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).

Source : oai:HAL:hal-01196858v1

Volume: Vol. 17 no. 1

Section: Discrete Algorithms

Published on: March 28, 2015

Submitted on: February 18, 2013

Keywords: Kolmogorov complexity,matching,graph colouring,performance measure,approximation algorithm,optimisation,algorithms,cost-effectiveness,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[INFO.INFO-HC] Computer Science [cs]/Human-Computer Interaction [cs.HC]

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