NP-completeness of the bulk synchronous task scheduling problem and its approximation algorithm

The bulk synchronous task scheduling problem (BSSP) is known as an effective task scheduling problem for distributed-memory machines, but the time complexity of BSSP is unknown. This paper presents a proof of NP-completeness of BSSP even in the case of unit time tasks and positive integer constant communication delays. This paper also gives an approximation algorithm for BSSP in several restricted cases.