Efficient approximation of twin-width

Develop an efficient algorithm that, given a graph of twin-width $d$, computes a contraction sequence of width bounded by a function of $d$, including an XP-time approximation algorithm as a minimum target.

Background

Fixed-parameter model-checking algorithms for graphs supplied with bounded-width contraction sequences are known. The survey emphasizes that obtaining such a contraction sequence from the graph itself is unresolved, even when the exponent of the running time may depend on the twin-width.