An FPT Algorithm for Maximum-Weight Independent Set in Embedded Graphs, in Lean 4
A Lean 4 and Mathlib formalization of a fixed-parameter theorem of "Maximum-weight independent set in embedded graphs parameterized by Euler genus and number of odd faces" (forthcoming), with a provably correct implementation of the algorithm as one fixed program for an explicit sixteen-register pointer machine. Lean proves that for every graph drawn in a closed surface of Euler genus gamma whose complement has k regions of odd total boundary length, and all integer vertex weights, the program outputs a maximum-weight independent set within 2^(c (p size(p) + 1)) (N size(M))^c bit operations,…
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