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Algorithmica

, Volume 81, Issue 9, pp 3803–3841 | Cite as

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

  • R. KrithikaEmail author
  • Abhishek Sahu
  • Saket Saurabh
  • Meirav Zehavi
Original Research
  • 7 Downloads

Abstract

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 \(\mathcal {O}(2^{\mathcal {O}(t \log t)} n^{\mathcal {O}(1)})\) 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.

Keywords

Cycle packing Proper interval deletion set Fixed-parameter tractable 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • R. Krithika
    • 1
    Email author
  • Abhishek Sahu
    • 2
  • Saket Saurabh
    • 2
    • 3
  • Meirav Zehavi
    • 4
  1. 1.Indian Institute of TechnologyPalakkadIndia
  2. 2.The Institute of Mathematical Sciences, HBNIChennaiIndia
  3. 3.University of BergenBergenNorway
  4. 4.Ben-Gurion UniversityBeershebaIsrael

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