A Golden Ratio Parameterized Algorithm for Cluster Editing
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 well-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.
KeywordsSearch Tree Input Graph Parity Property Golden Ratio Polynomial Factor
Unable to display preview. Download preview PDF.
- 14.Marx, D., Razgon, I.: Fixed-parameter tractability of multicut parameterized by the size of the cutset. In: Proc. of ACM Symposium on Theory of Computing, STOC 2011, pp. 469–478. ACM (2011), doi:10.1145/1993636.1993699Google Scholar
- 15.Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press (2006)Google Scholar
- 17.Rosamond, F. (ed.): FPT News: The Parameterized Complexity Newsletter (Since 2005), http://fpt.wikidot.com/