Abstract
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.
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Liberti, L., Raimondi, F. (2008). The Secret Santa Problem. In: Fleischer, R., Xu, J. (eds) Algorithmic Aspects in Information and Management. AAIM 2008. Lecture Notes in Computer Science, vol 5034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68880-8_26
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DOI: https://doi.org/10.1007/978-3-540-68880-8_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-68865-5
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