On a polyhedral target, one finite set of points locates the maximum of every monotone max–min combination of functions that share a convex part and differ by affine terms, whatever the rule and the shared part; a maximiser on an f-dimensional face is fixed by f+1 of the functions. For sensing disks this gives exact rational coverage radii and power thresholds for every monotone failure rule, the whole radius–budget frontier, a canonical certificate of minimal contact sets with witnesses, exact robust tests under independent placement errors and dual certificates for protection. This archive holds the LaTeX source, the compiled paper and the exact-arithmetic checks of the worked examples.
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Bhattacharjee et al. (2026) studied this question.
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