The Secret Santa Problem
Consider a digraph where the vertices represent people and an arc (i,j) represents the possibility of i giving a gift to j. The basic question we pose is whether there is an anonymity-preserving “gift assignment” such that each person makes and receives exactly one gift, and such that no person i can infer the remaining gift assignments from the fact that i is assigned to give a gift to j. We formalize this problem as a graph property involving vertex disjoint circuit covers, give a polynomial algorithm to decide this property for any given graph and provide a computational validation of the algorithm.
KeywordsAcceptable Solution Polynomial Algorithm ILOG CPLEX Connected Digraph Bipartite Digraph
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