An XP Algorithm for Maximum-Weight Independent Set in Embedded Graphs, in Lean 4
A Lean 4 and Mathlib formalization of Theorem 1 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 rational vertex weights, the program outputs a maximum-weight independent set within f(gamma + k) * N^(D(gamma, k) + C) * (L + 1)^b bit operations,…
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