Algorithm 2. Pseudocode for the proposed Fair Hungarian algorithm

$G=(X\cup Y,E)$

$\begin{array}{l}W=\mathrm{sort}(\{w(e_{xy})|x\in X,y\in Y\}\\ l=1\\ r=\left|W\right|\\ \mathrm{while}l\ne r\\ \hspace{1em}m=ceil(\frac{l+r}{2})\\ \hspace{1em}{E}_o=E-\left\{e_{xy}\right|w(e_{xy})>W(m),x\in X,y\in Y\}\\ \hspace{1em}\mathrm{if}\left|S\right|\ge \left|N(S)\right|\mathrm{for}S\subseteq X\\ \hspace{1em}\hspace{1em}r=m-1\\ \hspace{1em}\mathrm{else}\\ \hspace{1em}\hspace{1em}l=m\\ \mathrm{done}\\ E_o=E-\left\{e_{xy}\right|w(e_{xy})>W(l),x\in X,y\in Y\}\end{array}$

$\widehat{G}=(X\cup Y,E_o)$

$M$ = Hungarian-Algorithm ( $\widehat{G}$ )

$L$ = Layer ( $M$ )