Question: please explain . (3) Consider the following algorithm for finding a stable matching in a complete bipartite graph. Gale-Shapely Algorithm for Stable Matchings in Complete

 please explain . (3) Consider the following algorithm for finding a

stable matching in a complete bipartite graph. Gale-Shapely Algorithm for Stable Matchings

please explain .

(3) Consider the following algorithm for finding a stable matching in a complete bipartite graph. Gale-Shapely Algorithm for Stable Matchings in Complete Bipartite Graphs Input: a complete bipartite graph G (D,P, E) with D (di,ds. ..ds) and P ph, .. P Dd1, d2,.dkf an . for each 1 i k, di's ranking of elements of P: qi >?>?> > q? . for each 1 si s k, p's ranking of elements of D: fi>f>f P1,P2,...Pk (k?0) Output: A stable matching M Step 1: Let M0 Step 2: Let l be the least positive integer such that de is not matched in M. Let j be the least positive integer such that either . p, is unmatched; or dip, E M for some 1 siS k and p, prefers' de to d Step 3: If p, is unmatched, form M' by adding dep, to M. Otherwise, form M' by removing dip, from M and adding depj. Step 4: If IM,|-k, then output M'. Otherwise, let M-M, and go to Step 2

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