atomic decomposition of precedence graphs in distributed tasks scheduling

Task scheduling in distributed systems is a challenging NP-hard problem. This paper proposes a structural decomposition approach based on rank intervals derived from the precedence matrix. Tasks are grouped into atomic subsets using interval overlaps, enabling a reduction of the scheduling problem. A local ILP formulation is applied within each subset while preserving global precedence constraints. Experimental results show that the proposed approach reduces the problem complexity while maintaining solution quality.