2012/01/15 by Robert Ganian, Ganian, Robert · 2 citations
Computer Science · #Advanced Graph Theory Research #Complexity and Algorithms in Graphs #Computational Complexity (cs.CC) #Constraint Satisfaction and Optimization #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences
paper · pdf · doi:10.48550/arxiv.1201.3091
openalex publication_date 2012/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Parameterized algorithms are a very useful tool for dealing with NP-hard problems on graphs. Yet, to properly utilize parameterized algorithms it is necessary to choose the right parameter based on the type of problem and properties of the target graph class. Tree-width is an example of a very successful graph parameter, however it cannot be used on dense graph classes and there also exist problems which are hard even on graphs of bounded tree-width. Such problems can be tackled by using vertex cover as a parameter, however this places severe restrictions on admissible graph classes. Michael Lampis has recently introduced neighborhood diversity, a new graph parameter which generalizes vertex cover to dense graphs. Among other results, he has shown that simple parameterized algorithms exist for a few problems on graphs of bounded neighborhood diversity. Our article further studies this area and provides new algorithms parameterized by neighborhood diversity for the p-Vertex-Disjoint Paths, Graph Motif and Precoloring Extension problems -- the latter two being hard even on graphs of bounded tree-width.