Before revision:  To evaluate our algorithm empirically against existing heuristics, we introduce the 1D-VBR format, a specialization of VBRformat where columns are left ungrouped. We evaluate our algorithms on all 1626 real-valued matrices in the SuiteSparse Matrix Collection. When asked to minimize an empirically derived cost model for a sparse matrix-vector multiplication kernel, our algorithm produced partitions whose 1D-VBR realizations achieve a speedup of at least 1.18 over an unblocked kernel on 25\% of the matrices, and a speedup of at least 1.59 on 12.5\% of the matrices.
After revision:  To evaluate our algorithm empirically against existing heuristics, we introduce the 1D-VBR , which achieves better performance than VBR by only grouping rows. We describe detailed cost models for runtime and memory consumption. Then, we describe a linear time dynamic programming solution for optimally grouping the rows for 1D-VBR realizations achieve a speedup of at least 1.18 over an unblocked kernel on 25\% of the matrices, and a speedup of at least 1.59 on 12.5\% of the matrices.