The Secret Santa Problem

  • Authors:

  • Leo Liberti;Franco Raimondi

  • Affiliations:

  • LIX, École Polytechnique, Palaiseau, France F-91128;Dept. of Computer Science, University College London, UK

  • Venue:
  • AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
  • Year:
  • 2008

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Abstract

Consider a digraph where the vertices represent people and an arc (i,j) represents the possibility of igiving 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 ican infer the remaining gift assignments from the fact that iis 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.