Domino sequencing: Scheduling with state-based sequence-dependent setup times

We introduce the Domino Sequencing problem, a scheduling problem with special sequence-dependent setup times. For each job there are corresponding start and end states and . When job is scheduled immediately before job , a setup time of 1 is needed if . We present polynomial-time algorithms for various versions. When jobs are partitioned into families, we show that the problem becomes -hard and present a fixed-parameter tractable algorithm.