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

This paper explores ways of performing commutative tasks by N parties. Tasks are defined as commutative if the order at which parties perform tasks 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 this conjecture. We also explore the most equitable commutative task protocols.