Following When comparing Δ𝐻𝐻 calculated from different algorithms, a difference of more than 10 -5 eV/atom is considered nonzero unless specified otherwise. The free academic version of Gurobi 9.5, along with its Python bindings, is used to solve the linear minimization defined by eq. 3. Detailed implementation, instructions, and figures generated for this study are available through a GitHub repository at . our "diligent" version of the greedy algorithm (Diligent-F3). Figure shows the distribution of nonzero difference (with a tolerance of 10 -5 eV/atom) in calculated reaction enthalpies between the two versions, Δ𝐻𝐻 Diligent-F3 -Δ𝐻𝐻 Lazy-F3 , where a negative value indicates the diligent version is better. Diligent-F3 finds a lower reaction enthalpy more frequently than its Lazy counterpart, which also holds for Diligent-All (see Figure ). Key characteristics of the distributions of Δ𝐻𝐻 Diligent -Δ𝐻𝐻 Lazy are summarized in Table . While data from Materials Project suggest the diligent version is preferred over the lazy one, this may not be true for other datasets. For example, from randomly generated oxidation reactions (see Figure ), we found a much more symmetric distribution of nonzero Δ𝐻𝐻 ox Diligent-All -Δ𝐻𝐻 ox Lazy-All , indicating no clear benefits to using one version of the greedy algorithm over another. The central result of this paper is the comparison of greedy algorithms and linear programming for the oxidation reactions identified from Materials Project (Figure ). For both Lazy-F3 and Diligent-F3, all Δ𝐻𝐻 ox 𝐿𝐿𝐿𝐿 ≤ 𝐻𝐻 ox Greedy . This also holds true for both Lazy-All and Diligent-All (Figure ), indicating that linear programming always finds a solution better than (or equal to) the one returned by the greedy algorithms. Iterating over all possible first choices significantly improves the results from greedy algorithms, as both nonzero Δ𝐻𝐻 ox LP -Δ𝐻𝐻 ox Lazy-All and nonzero Δ𝐻𝐻 ox LP -Δ𝐻𝐻 ox Diligent-All show distributions (Figure ) narrower than their counterparts, respectively (Table ). The distributions of reaction enthalpies for all calculation methods are qualitatively similar (Figure ). They all have a major peak at around -5.5 eV/atom and two satellite peaks near -1.3 eV/atom and 1.0 eV/atom, respectively, corresponding to compounds containing F, Cl, Br.