Parameterized complexity of machine scheduling: 15 open problems

Machine scheduling problems are a long-time key domain of algorithms and complexity research. A novel approach to machine scheduling problems are fixed-parameter algorithms. To stimulate this thriving research direction, we propose 15 open questions in this area whose resolution we expect to lead to the discovery of new approaches and techniques both in scheduling and parameterized complexity theory.Comment: Version accepted to Computers & Operations Researc

High Multiplicity Scheduling on One Machine with Forbidden Start and Completion Times

We are interested in a single machine scheduling problem where no task can either start or end on some dates and the input is given using a compact encoding. The aim is to minimize the makespan. We present a polynomial time algorithm for large diversity instances (when the number of different processing times is bigger than the number of forbidden dates). We also show that this problem is fixed parameter tracktable when the number of forbidden dates is fixed, regardless of tasks characteristics

High-multiplicity scheduling on one machine with forbidden start and completion times

International audienceWe are interested in a single machine scheduling problem where jobs can neither start nor end on some specified instants, and the aim is to minimize the makespan. This problem models the situation where an additional resource, subject to unavailability constraints, is required to start and to finish a job. We consider in this paper the high-multiplicity version of the problem, when the input is given using a compact encoding. We present a polynomial time algorithm for large diversity instances (when the number of different processing times is greater than the number of forbidden instants). We also show that this problem is fixed-parameter tractable when the number of forbidden instants is fixed, regardless of jobs characteristics