Abstract
Vertex Covering by Paths on Trees with applications in machine translation is the task to cover all vertices of a tree T = ( V , E ) by choosing a minimum-weight subset of given paths in the tree. The problem is NP-hard and has recently been solved by an exact algorithm running in O ( 4 C ⋅ | V | 2 ) time, where C denotes the maximum number of paths covering a tree vertex. We improve this running time to O ( 2 C ⋅ C ⋅ | V | ) . On the route to this, we introduce the problem Tree-like Weighted Hitting Set which might be of independent interest. In addition, for the unweighted case of Vertex Covering by Paths on Trees, we present an exact algorithm using a search tree of size O ( 2 k ⋅ k ! ) , where k denotes the number of chosen covering paths. Finally, we briefly discuss the existence of a size- O ( k 2 ) problem kernel.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
