Coupled-tasks in presence of bipartite compatibilities graphs

Abstract. We tackle the makespan minimization coupled-tasks prob-lem in presence of incompatibility constraints. In particular, we focus on stretched coupled-tasks, i.e.coupled-tasks having the same sub-tasks execution time and idle time duration. We study several problems in the framework of classic complexity and approximation for which the compatibility graph is bipartite (star, chain,...). In such context, we design efficient polynomial-time approximation algorithms according to different parameters of the scheduling problem.