TY - JOUR
T1 - The Parameterized Complexity of Cycle Packing
T2 - Indifference is Not an Issue
AU - Krithika, R.
AU - Sahu, Abhishek
AU - Saurabh, Saket
AU - Zehavi, Meirav
N1 - Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2019/9/16
Y1 - 2019/9/16
N2 - In the Cycle Packing problem, we are given an undirected graph G, a positive integer r, and the task is to check whether there exist r vertex-disjoint cycles. In this paper, we study Cycle Packing with respect to a structural parameter, namely, distance to proper interval graphs (indifference graphs). In particular, we show that Cycle Packing is fixed-parameter tractable (FPT) when parameterized by t, the size of a proper interval deletion set. For this purpose, we design an algorithm with O(2 O ( t log t )nO ( 1 )) running time. Bodlaender et al. (Theor Comput Sci 511:117–136, 2013) studied several structural parameterizations for Cycle Packing and our FPT algorithm fills a gap in their ecology of parameterizations. We combine color coding, greedy strategy and dynamic programming based on structural properties of proper interval graphs in a non-trivial fashion to obtain the FPT algorithm. Our belief is that this approach is quite general and can be useful in solving many other problems with the same parameterization.
AB - In the Cycle Packing problem, we are given an undirected graph G, a positive integer r, and the task is to check whether there exist r vertex-disjoint cycles. In this paper, we study Cycle Packing with respect to a structural parameter, namely, distance to proper interval graphs (indifference graphs). In particular, we show that Cycle Packing is fixed-parameter tractable (FPT) when parameterized by t, the size of a proper interval deletion set. For this purpose, we design an algorithm with O(2 O ( t log t )nO ( 1 )) running time. Bodlaender et al. (Theor Comput Sci 511:117–136, 2013) studied several structural parameterizations for Cycle Packing and our FPT algorithm fills a gap in their ecology of parameterizations. We combine color coding, greedy strategy and dynamic programming based on structural properties of proper interval graphs in a non-trivial fashion to obtain the FPT algorithm. Our belief is that this approach is quite general and can be useful in solving many other problems with the same parameterization.
KW - Cycle packing
KW - Fixed-parameter tractable
KW - Proper interval deletion set
UR - http://www.scopus.com/inward/record.url?scp=85068179716&partnerID=8YFLogxK
U2 - 10.1007/s00453-019-00599-0
DO - 10.1007/s00453-019-00599-0
M3 - Article
AN - SCOPUS:85068179716
VL - 81
SP - 3803
EP - 3841
JO - Algorithmica
JF - Algorithmica
SN - 0178-4617
IS - 9
ER -