SQLite
From OpenStreetMap Wiki
Is a local Database Management System that has a Geo Extension calles SpatiaLite, too. Cause it has no complex DBMS and structures, it will fail on bigger data extracs.
The routing function is among those supported.
- ([1]) contains information on using it with the OpenStreetMap data, and this tutorial
- ([2]) has instructions on how to perform both routing and rendering using OpenStreetMap data.
Microcosm is a map API server that uses Sqlite and the R*tree module.