Shrink the Range, Keep the Distance
TL;DR for operators If every conflicting pair in an allocation system must already be separated by at least $k$ units, the unresolved question is often not how far apart assignments can be pushed. It is how little total capacity is required to satisfy that rule. Hieu Truong Xuan and Khanh To Van formalize that question as Minimum Span Antibandwidth Labeling and Minimum Span Cyclic Antibandwidth Labeling.1 For a fixed separation requirement, feasibility moves monotonically with the candidate label-domain size: once a candidate range is large enough, every larger one is feasible as well. That structure lets an exact solver treat capacity as an ordered sequence of feasibility tests rather than a generic optimization variable. ...