We consider the setting of online computation with advice, and study the bin packing problem and a number of scheduling problems. We show that it is possible, for any of these problems, to arbitrarily approach a competitive ratio of 1 with only a constant number of bits of advice per request. For the bin packing problem, we give an online algorithm with advice that is (1 + ε)-competitive and uses O 1 ε log 1 ε bits of advice per request. For scheduling on m identical machines, with the objective function of any of makespan, machine covering and the minimization of the ℓp norm, p > 1, we give similar results. We give online algorithms with advice which are (1 + ε)-competitive ((1/(1 − ε))-competitive for machine covering) and also use O 1 ε log 1 ε bits of advice per request. We complement our results by giving a lower bound showing that for any online algorithm with advice to be optimal, for any of the above scheduling problems, a non-constant number (namely, at least 1 − 2m n log m, where n is the number of jobs and m is the number of machines) of bits of advice per request is needed.
Renault et al. REF present a LAAS for the Bin Packing problem, and for a family of scheduling problems on m identical machines that includes the objectives of minimizing the makespan, minimizing the p norm, and machine covering.
Online Algorithms with Advice for Bin Packing and Scheduling Problems
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Computer Science