Machine Covering in the Random-Order Model

In the Online Machine Covering problem, jobs, defined by their sizes, arrive one and have to be assigned m parallel identical machines, with goal of maximizing load least-loaded machine. Unfortunately, classical model allows only fairly pessimistic performance guarantees: The best possible deterministic ratio is achieved Greedy-strategy, known randomized algorithm has competitive $${\tilde{O}}(\sqrt{m})$$ , which cannot improved more than a logarithmic factor. Modern results try mitigate this studying semi-online models, where additional information about job sequence revealed in advance or extra resources are provided online algorithm. work, we study problem recently popular random-order model. Here, no present but, instead, adversary weakened that it can decide upon input set while jobs uniformly at random. It particularly relevant lower bounds usually associated highly structured sequences. We first analyze Graham’s Greedy-strategy context establish its decreases slightly $$\Theta \left( \frac{m}{\log (m)}\right) $$ asymptotically tight. Then, as our main result, an $${\tilde{O}}(\root 4 \of {m})$$ -competitive for problem. This result exploiting coming from random order using sampling techniques devise mechanism distinguish relatively large small ones. complement bound, showing $$O\left( \frac{\log (m)}{\log \log bound novel variant Secretary could independent interest.