Every decision exposed.

Every feasible subset is checked. The returned set maximizes the stated objective within floating-point tolerance. Ties prefer lower cost, then the ID-sorted subset mask.

A separate density-greedy search with add/drop/exchange repair is compared with that exact answer. The displayed gap is measured, never assumed to be zero.

Enumeration is exponential: O(n·2ⁿ) time and O(2ⁿ) memory. The 18-candidate limit is intentional. This objective is a design choice, not a universal definition of usefulness.

The first eight observations initialize the reference. Each subsequent score uses the median and median absolute deviation of accepted earlier values. Suspected anomalies do not contaminate the reference.

A short run becomes a spike when a later value returns inside the envelope or changes direction. A sustained run becomes a shift at confirmation. Its earlier points are then relabeled retrospectively. Unfinished tails remain pending.

Slow drift, periodic signals, bad warm-up data, and bursts longer than the confirmation length can fool this detector. It is a deterministic heuristic, not a calibrated statistical test. Scores are not probabilities.

O(n·w log w) time with this sorting-based reference; O(w+p) detector state, plus O(n) output for the chart.

Each key–worker pair gets a deterministic cost −ln(U)/weight from SHA-256. Add the migration price when an existing key moves. A min-cost flow solver finds a capacity-feasible global minimum of costs quantized to 10⁻⁶.

This plans a batch; it does not move data. Affinity is a hash preference, not measured network latency. It assumes equal-size keys and complete eligibility across workers. It does not model replicas, fault domains, or per-key memory.

A dense residual graph gives O(K·(K+W)²) time and O((K+W)²) memory. The input limits keep this lab bounded.