The Parameterized Complexity of Cycle Packing: Indifference is Not an Issue

R. Krithika, Abhishek Sahu, Saket Saurabh, Meirav Zehavi

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish
Pages (from-to)3803-3841
Number of pages39
Issue number9
StatePublished - 16 Sep 2019


  • Cycle packing
  • Fixed-parameter tractable
  • Proper interval deletion set

ASJC Scopus subject areas

  • Computer Science (all)
  • Computer Science Applications
  • Applied Mathematics


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