Efficient parameterized algorithms by number of reconfiguration steps

Determine whether the Layered Connectivity Shortest Reconfiguration decision problem—given two always-connected temporal graphs G1 and G2 and an integer l, decide if there is a valid reconfiguration sequence of length at most l—admits efficient parameterized algorithms when parameterized by l (the number of reconfiguration steps), and, if so, construct such algorithms.

Background

The paper introduces the Layered Connectivity Reconfiguration problem on always-connected temporal graphs and provides a polynomial-time algorithm for deciding reconfigurability and constructing a valid sequence of edge relabelings, as well as an NP-hardness result for finding a shortest reconfiguration sequence via a reduction from Vertex Cover.

In the conclusion, the authors highlight further directions, including parameterized variants. A specific open question asks whether efficient algorithms can be obtained by parameterizing by the number of reconfiguration steps, which directly targets the parameterized complexity of the length-bounded decision problem (Layered Connectivity Shortest Reconfiguration) defined in the paper.