Parameterized complexity of rank-1 and rank-2 wildcard decomposition

Characterize the parameterized complexity of rank-1 and rank-2 tensor decomposition with wildcard entries when parameterized by the number of wildcard elements in the input tensor, determining whether these problems are fixed-parameter tractable or complete for standard parameterized complexity classes.

Background

The paper provides a polynomial-time algorithm for rank-1 wildcard decomposition over a fixed finite field and establishes NP-hardness for rank-2 with wildcards over Z/2Z. Investigating parameterized complexity relative to the wildcard count could yield finer-grained complexity classifications and potential algorithmic tractability under bounded wildcard regimes.