Chapter

Open Problems in Mathematics and Computational Science

pp 317-340

Date:

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

  • Eric BrierAffiliated withIngenico Email author 
  • , David NaccacheAffiliated withÉcole normale supérieure, Département d’informatique
  • , Li-yao XiaAffiliated withÉcole normale supérieure, Département d’informatique

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Abstract

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.