Shortest Common Superstrings and Scheduling with Coordinated Starting Times

In the first part of this paper we show that the Shortest Common Superstring problem is NP-complete even if all strings are of the simple form 10plOq, p,q E N. This result closes the gap left between the polynomial cases where all strings are of the form Op104 or all strings are of the form lop1 and NP-complete cases when strings have a more complicated structure. In the second part of the paper we use the above result to investigate the complexity of 2-machine flow-shop and open-shop problems with machines that have to coordinate their starting times, i.e. when one machine starts an operation the other machine also starts an operation or has to be idle at that time.