Abstract

We discuss what we consider to be the ten most vexing open questions in the area of polynomial time approximation algorithms for NP-hard deterministic machine scheduling problems. We summarize what is known on these problems, we discuss related results, and we provide pointers to the literature. Prologue In the early days of scheduling, the work of the theoretical research branch mainly consisted of classifying scheduling problems into easy (i.e., polynomially solvable) and hard (i.e., NP- hard) ones. Nowadays, researchers have become interested in a better understanding and a much finer classification of the hard problems; one very active branch of research classifies hard scheduling problems according to their approximability. In the sequel, we summarize and discuss what in our opinion are the most outstanding open questions in the approximation of scheduling problems. Throughout the paper, we use the standard three-field scheduling notation (see e.g. Graham, Lawler, Lenstra & R...

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