Scheduling under Uncertainty: A Query-based Approach

Scheduling under Uncertainty: A Query-based Approach

Luciana Arantes, Evripidis Bampis, Alexander Kononov, Manthos Letsios, Giorgio Lucarelli, Pierre Sens

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence
Main track. Pages 4646-4652. https://doi.org/10.24963/ijcai.2018/646

We consider a single machine, a set of unit-time jobs, and a set of unit-time errors. We assume that the time-slot at which each error will occur is not known in advance but, for every error, there exists an uncertainty area during which the error will take place. In order to find if the error occurs in a specific time-slot, it is necessary to issue a query to it. In this work, we study two problems: (i) the error-query scheduling problem, whose aim is to reveal enough error-free slots with the minimum number of queries, and (ii) the lexicographic error-query scheduling problem where we seek the earliest error-free slots with the minimum number of queries. We consider both the off-line and the on-line versions of the above problems. In the former, the whole instance and its characteristics are known in advance and we give a polynomial-time algorithm for the error-query scheduling problem. In the latter, the adversary has the power to decide, in an on-line way, the time-slot of appearance for each error. We propose then both lower bounds and algorithms whose competitive ratios asymptotically match these lower bounds.
Keywords:
Planning and Scheduling: Scheduling
Planning and Scheduling: Planning with Incomplete information
Uncertainty in AI: Nonprobabilistic Models
Agent-based and Multi-agent Systems: Resource Allocation