A Golden Ratio Parameterized Algorithm for Cluster Editing [chapter]

Sebastian Böcker
2011 Lecture Notes in Computer Science  
The Cluster Editing problem asks to transform a graph by at most k edge modifications into a disjoint union of cliques. The problem is NP-complete, but several parameterized algorithms are known. We present a novel search tree algorithm for the problem, which improves running time from O * (1.76 k ) to O * (1.62 k ). In detail, we can show that we can always branch with branching vector (2, 1) or better, resulting in the golden ratio as the base of the search tree size. Our algorithm uses a
more » ... -known transformation to the integer-weighted counterpart of the problem. To achieve our result, we combine three techniques: First, we show that zero-edges in the graph enforce structural features that allow us to branch more efficiently. Second, by repeatedly branching we can isolate vertices, releasing costs. Finally, we use a known characterization of graphs with few conflicts. This is a preprint of: Sebastian Böcker. A golden ratio parameterized algorithm for Cluster Editing.
doi:10.1007/978-3-642-25011-8_7 fatcat:kif6oj3r6bfenlkubucyvnrfoa