Cost-effectiveness of algorithms

Graham Farr (1)

1 Faculty of Information Technology [Clayton]

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).

Mots clés: optimisation; algorithms; cost-effectiveness; approximation algorithm; performance measure; graph colouring; matching; Kolmogorov complexity

Domaines: Mathématique discrète [cs.DM]; Interface homme-machine [cs.HC]

Graham Farr. Cost-effectiveness of algorithms. Discrete Mathematics and Theoretical Computer Science, 2015, Vol. 17 no. 1 (1), pp.201--218. ⟨10.46298/dmtcs.2114⟩. ⟨hal-01196858⟩