Randomized algorithms
On the efficiency of polynomial time approximation schemes
Information Processing Letters
Approximation schemes for constrained scheduling problems
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
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Data generation for computational testing of optimization algorithmsis a key topic in experimental algorithmics. Recently, concern has arisen that many published computational experiments are inadequate respect to the way test instances are generated. In this paper we suggest a new research direction that might be useful to cope with the possible limitations of data generation. The basic idea is to select a finite set of instances which 'represent' the whole set of instances. We propose a measure of the representativeness of an instance, which we call Ɛ-representativeness: for a minimization problem, an instance xƐ is e-representative of another instance x if a (1 + Ɛ)-approximate solution to x can be obtained by solving xƐ. Focusing on a strongly NP-hard single machine scheduling problem, we show how to map the infinite set of all instances into a finite set of Ɛ-representative core instances. We propose to use this finite set of Ɛ-representative core instances to test heuristics.