Improved parameterized algorithms by number of leaves

Determine whether the parameterized algorithms for generalized search-tree recognition of Maximum Cardinality Search and Maximal Neighborhood Search, parameterized by the number of leaves of the given spanning tree, can be improved to the running time sought by the paper.

Background

The paper discusses parameterized algorithms for generalized search-tree recognition in terms of the number of leaves of the input spanning tree. Existing results for Maximum Cardinality Search and Maximal Neighborhood Search follow from parameterized algorithms for the Partial Search Order Problem, but the authors explicitly leave open whether these running-time bounds can be improved. The target running-time expression is displayed mathematically in the source but is not recoverable from the supplied text extraction.