Direct updates usually beat tiled reuse for changing sparse inputs

When only some input rows change, an incremental calculation can avoid recomputing an entire sparse-matrix product. But the changed rows may move from step to step, making a prepared schedule less useful.

When does reusing that schedule save time over updating directly from the changed rows' matrix columns?

The authors separate persistent tile preparation from exact tile-set reuse, then test when tiled updates can beat direct column updates.

For a fixed sparse matrix and changing input rows, when does reusing a tiled schedule save time over updating directly by column? The answer matters because changed rows can move between steps, while a prepared schedule may no longer match them.

The authors compare the approaches on identical update streams. Direct compressed sparse column (CSC) updates beat the tiled executor in 779 of 837 moving sessions, supporting the conclusion that tiling usually did not pay on these workloads.

The exceptions clustered in one matrix family, where tiles combined contributions into fewer output writes.

The primary timing study used one CPU core and one tiled executor on a preselected set of 21 matrices. The held-out test supports the structural explanation within the TSOPF matrix family; it does not establish the same result for other matrix structures, executors or platforms.