One embodiment of the present invention sets forth a technique for synchronizing the execution of multiple cooperative thread arrays (CTAs) implementing a parallel algorithm that is mapped onto a graphics processing unit. An array of semaphores provides synchronization status to each CTA, while one designated thread within each CTA provides updated status for the CTA. The designated thread within each participating CTA reports completion of a given computational phase by updating a current semaphore within the array of semaphores. The designated thread then polls the status of the current semaphore until all participating CTAs have reported completion of the current computational phase. After each CTA has completed the current computational phase, all participating CTAs may proceed to the next computational phase.