Error compensation in leaf root problems

Authors:
Michael Dom;Jiong Guo;Falk Hüffner;Rolf Niedermeier
Affiliations:
Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Tübingen, Fed Rep of, Germany;Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Tübingen, Fed Rep of, Germany;Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Tübingen, Fed Rep of, Germany;Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Tübingen, Fed Rep of, Germany
Venue:
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Year:
2004

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Abstract

The k-Leaf Root problem is a particular case of graph power problems Here, we study “error correction” versions of k-Leaf Root—that is, for instance, adding or deleting at most l edges to generate a graph that has a k-leaf root We provide several NP-completeness results in this context, and we show that the NP-complete Closest 3-Leaf Root problem (the error correction version of 3-Leaf Root) is fixed-parameter tractable with respect to the number of edge modifications in the given graph Thus, we provide the seemingly first nontrivial positive algorithmic results in the field of error compensation for leaf root problems with k 2 To this end, as a result of independent interest, we develop a forbidden subgraph characterization of graphs with 3-leaf roots.