5 research outputs found
Unit Interval Editing is Fixed-Parameter Tractable
Given a graph~ and integers , , and~, the unit interval
editing problem asks whether can be transformed into a unit interval graph
by at most vertex deletions, edge deletions, and edge
additions. We give an algorithm solving this problem in time , where , and denote respectively
the numbers of vertices and edges of . Therefore, it is fixed-parameter
tractable parameterized by the total number of allowed operations.
Our algorithm implies the fixed-parameter tractability of the unit interval
edge deletion problem, for which we also present a more efficient algorithm
running in time . Another result is an -time algorithm for the unit interval vertex deletion problem,
significantly improving the algorithm of van 't Hof and Villanger, which runs
in time .Comment: An extended abstract of this paper has appeared in the proceedings of
ICALP 2015. Update: The proof of Lemma 4.2 has been completely rewritten; an
appendix is provided for a brief overview of related graph classe