Polynomial-time computation of bounded twin-width contraction sequences

Determine whether a polynomial-time algorithm exists that computes a suitable contraction sequence witnessing bounded twin-width for an input graph.

Background

Fixed-parameter tractable first-order model checking on bounded-twin-width classes requires the input graph to be accompanied by a contraction sequence witnessing the bounded twin-width. The paper notes that the existence of an efficient algorithm for computing such a sequence is unresolved, creating an algorithmic input-certification problem for the twin-width model-checking theorem.