On a Synchronization Problem With Multiple Instances

We study a synchronization problem with multiple instances. First, we show that the problem we consider can be formulated as the problem of finding an intra-column rearrangement for multiple matrices (which reflect problem instances) such that the row sums across the various matrices show minimum variability. To obtain the optimal rearrangement, we introduce the Block Swapping Algorithm (BSA) and a further customization of it that we label as the Customized Block Swapping Algorithm (Cust BSA). A numerical study shows that the two algorithms we propose yield high-quality solutions and also deal efficiently with high-dimensional set-ups.