TY - GEN

T1 - Unit interval editing is fixed-parameter tractable

AU - Cao, Yixin

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=84950134089&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-47672-7_25

DO - 10.1007/978-3-662-47672-7_25

M3 - Conference article published in proceeding or book

SN - 9783662476710

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 306

EP - 317

BT - Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings

PB - Springer Verlag

T2 - 42nd International Colloquium on Automata, Languages and Programming, ICALP 2015

Y2 - 6 July 2015 through 10 July 2015

ER -