Linear growth of bottleneck error for dependent deletions

Determine whether there exists a family of interacting generator deletions for which the bottleneck error grows linearly with the number of deletions, thereby making the additive sum-of-costs bound essentially sharp.

Background

For independent deletion families, the paper proves that the bottleneck error is bounded by the maximum deletion cost, whereas the sequential guarantee for interacting deletions is the sum of their costs. Experiments show that short dependent sequences can nearly attain this sum, but longer sequences in the sampled runs exhibit substantially smaller errors relative to the additive bound.

The unresolved issue is whether this subadditive behavior persists in general or whether some family of dependent deletions can force the cumulative bottleneck error to scale linearly with the number of deletions.