Kernelization and parameterized algorithms for covering a tree by a set of stars or paths

Two restricted versions of the Subforest Isomorphism problem, the Covering a Tree by a Set of Stars (CTSS) and the Covering a Tree by a Set of Paths (CTSP) problems, are studied. Both problems are NP-complete. The problems are closely related to a number of well-studied problems, including the problems Subgraph Isomorphism, Tree Editing, and Graph Packing. It is shown that the problems CTSS and CTSP are fixed-parameter tractable. Thorough development of parameterized algorithms and kernelization algorithms for these problems are presented.