Given a graph G and integers k1, k2, and k3, the unit interval editing problem asks whether G can be transformed into a unit interval graph by at most k1 vertex deletions, k2 edge deletions, and k3 edge additions. We give an algorithm solving the problem in 2O(klogk) ·(n+m) time, where k:= k1 +k2 +k3, and n, m denote respectively the numbers of vertices and edges of G. Therefore, it is fixed-parameter tractable parameterized by the total number of allowed operations. This implies the fixed-parameter tractability of the unit interval edge deletion problem, for which we also present a more efficient algorithm running in time O(4k · (n + m)). Another result is an O(6k · (n + m))-time algorithm for the unit interval vertex deletion problem, significantly improving the best-known algorithm running in time O(6k · n6).
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||42nd International Colloquium on Automata, Languages and Programming, ICALP 2015|
|Period||6/07/15 → 10/07/15|
- Computer Science(all)
- Theoretical Computer Science