Before revision:  We present a novel and efficient algorithm that finds the leximin optimal stable matching under ranked isometric utilities . To the best of our knowledge, we are the first to address the problem of finding a leximin optimally fair and stable matching .
After revision:  We present a novel and efficient algorithm that finds the leximin optimal stable matching under ranked isometric utilities (where the utilities from matching are the same across an edge). The running time of FaSt is linear in the number of edges. Additionally, we provide an efficient algorithm, called FaSt-Gen, that finds the leximin optimal stable matching for ranked but otherwise unconstrained utilities. The running time of FaSt-Gen is quadratic in the number of edges. We then establish that, in the absence of rankings, finding a leximin optimally fair and stable matching .