How to Sign Paper Contracts? Conjectures and Evidence Related to Equitable and Efficient Collaborative Task Scheduling

  • Eric Brier
  • David Naccache
  • Li-yao Xia


This chapter explores ways of performing a kind of commutative task by N parties, of which a particular scenario of contract signing is a canonical example. Tasks are defined as commutative if the order in which parties perform them can be freely changed without affecting the final result. It is easy to see that arbitrary N-party commutative tasks cannot be completed in less than N − 1 basic time units.

We conjecture that arbitrary N-party commutative tasks cannot be performed in N − 1 time units by exchanging less than 4N − 6 messages and provide computational evidence in favor of this conjecture. We also explore the most equitable commutative task protocols.



The authors thank Oğuzhan Külekci for interesting discussions and useful remarks notably concerning the variant of the traveling salesmen problem.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.IngenicoGuilherand-GrangesFrance
  2. 2.École normale supérieure, Département d’informatiqueParis Cedex 05France

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