Biomarker Panel Search Space

Systems biology keeps running into the same wall: many real questions — which minimal panel of genes explains a phenotype, which hub proteins hold a regulatory network together, which combination of markers predicts disease — are combinatorial searches over subsets of candidates, and checking every combination scales as 2ⁿ. This simulator times four genuine algorithms on the same synthetic gene-expression dataset — a linear mean, an O(n log n) sort, an O(n²) all-pairs correlation pass, and a real O(n·2ⁿ) brute-force subset-sum search for a target biomarker panel — and stacks each live measurement into a growing 3D skyline. Drag the shortlist size and re-run the benchmark to watch the exponential column race away from the polynomial ones, a direct, measured illustration of why P-time verification and NP-hard search are such different problems.