Replication in Graph Partitioning and Scheduling Problems

A new arXiv paper by Papp, Böhnlein, and Yzelman (arXiv:2605.00209) provides the first comprehensive analysis of task replication in graph partitioning and DAG scheduling problems. Traditionally, these models assume each node runs on a single processor. The authors show that allowing replication — running the same operation on multiple processors — can dramatically reduce inter-process communication costs. On the theoretical side, they prove that replication makes graph partitioning significantly harder to approximate, while scheduling complexity is less affected. This trade-off between increased computation and reduced communication is key to understanding when replication pays off.

Experiments using Integer Linear Programming (ILP) on real-world graphs reveal substantial cost reductions. For hypergraph partitioning, replication reduces communication costs by 17% to 65% on average, sometimes eliminating it entirely. For DAG scheduling, a sophisticated heuristic achieves mean reductions of 11.61%–23.13%, with individual cases reaching 58.17%. These results suggest that replication is a powerful, underutilized tool for optimizing parallel execution in distributed and cluster computing — especially as workloads grow larger and communication becomes the dominant bottleneck.