A central lemma used for all lower bounds in this scheduling paper, that chains with different skinny job lengths cannot overlap, is contradicted by a simple parallel schedule, so the claimed hardness and online lower bounds are not established.
On-line scheduling with precedence constraints
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Almost Tight Approximation Hardness and Online Algorithms for Resource Scheduling
A central lemma used for all lower bounds in this scheduling paper, that chains with different skinny job lengths cannot overlap, is contradicted by a simple parallel schedule, so the claimed hardness and online lower bounds are not established.