Change VariableOrdering so that indexing happens using integers rather than strings.

## 🚀 Feature

Current variable indexing uses string, which impacts efficiency.
## Motivation

Switching to integers under the hood may result in substantial speed up.

Start by locating the VariableOrdering implementation and its existing tests or benchmarks. Trace how variables are currently indexed, then define completion as preserving current behavior while changing the internal indexing representation from strings to integers and verifying the efficiency impact.

Written by the indexing model from the issue text.