Recompute only what changed.
Toll operators routing calls, Bell System, 1949
Delta Routing updates the output of a fixed operator, such as a matrix, a stencil, or a network, from the part of its input that changed, instead of recomputing it from the whole input. The cost follows the size of the change.
Measured envelope
p is the fraction of the input that changed between two updates. Up to p = 0.50 the update is faster; by p = 0.75, recomputing is.
| p | 0.01 | 0.04 | 0.16 | 0.32 | 0.50 | 0.75 | 1.00 |
|---|---|---|---|---|---|---|---|
| Speed | 75.06× | 17.66× | 3.94× | 1.79× | 1.09× | 0.72× | 0.54× |
Where the changes fall barely matters: at p = 0.01, contiguous, moving, and scattered changes measured 75.06× to 75.47×.
Flat column-packed delta against a full matrix-vector product (cblas_dgemv, tuned OpenBLAS 0.3.26, one thread). N = M = 1024, one right-hand side, f64, scattered changes. One pinned Intel i7-1165G7 core, g++ 13.3.0. Measured 11 August 2026.
Delta Routing for Ubuntu
A system package that routes the sparse matrix-vector calls of an unmodified binary through the delta path, so there is nothing to recompile.
- 39.25×
- against MKL on one thread
- 24.89×
- against a plain CSR loop
- 1.000×
- where the gate declined and the original MKL call ran
The first two figures come from the six cells where the changes formed one contiguous block that drifted between steps. Against MKL at its best thread count, those cells ran about 14× faster.
NUC11 with an Intel i7-1165G7, one core, MKL 2026.1.0 with MKL_NUM_THREADS=1. N = M = 400,000 with 3.16 million nonzeros, churn rate ρ ≤ 0.25. Measured 3 August 2026.
Bindings for Python, Java, C and C++, Rust, Go, .NET, and Node.js, and an Ubuntu system package. The community package is open source under Apache-2.0 at github.com/HorneSci/hst-studio.
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Tell us what the system does, how often it recomputes, and what it runs on.
