Document Open Access Logo

Parameterized and Approximation Algorithms for the Load Coloring Problem

Authors Florian Barbero, Gregory Gutin, Mark Jones, Bin Sheng



PDF
Thumbnail PDF

File

LIPIcs.IPEC.2015.43.pdf
  • Filesize: 495 kB
  • 12 pages

Document Identifiers

Author Details

Florian Barbero
Gregory Gutin
Mark Jones
Bin Sheng

Cite AsGet BibTex

Florian Barbero, Gregory Gutin, Mark Jones, and Bin Sheng. Parameterized and Approximation Algorithms for the Load Coloring Problem. In 10th International Symposium on Parameterized and Exact Computation (IPEC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 43, pp. 43-54, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/LIPIcs.IPEC.2015.43

Abstract

Let c, k be two positive integers. Given a graph G=(V,E), the c-Load Coloring problem asks whether there is a c-coloring varphi: V => [c] such that for every i in [c], there are at least k edges with both endvertices colored i. Gutin and Jones (IPL 2014) studied this problem with c=2. They showed 2-Load Coloring to be fixed-parameter tractable (FPT) with parameter k by obtaining a kernel with at most 7k vertices. In this paper, we extend the study to any fixed c by giving both a linear-vertex and a linear-edge kernel. In the particular case of c=2, we obtain a kernel with less than 4k vertices and less than 8k edges. These results imply that for any fixed c >= 2, c-Load Coloring is FPT and the optimization version of c-Load Coloring (where k is to be maximized) has an approximation algorithm with a constant ratio.
Keywords
  • Load Coloring
  • fixed-parameter tractability
  • kernelization

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. N. Ahuja, A. Baltz, B. Doerr, A. Prívetivý, and A. Srivastav. On the minimum load coloring problem. J. Discrete Algorithms, 5(3):533-545, 2007. Google Scholar
  2. J.-P. Allouche and J. Shallit. The ring of k-regular sequences, II. Theor. Comput. Sci., 307(1):3-29, 2003. Google Scholar
  3. H. L. Bodlaender, F. V. Fomin, D. Lokshtanov, E. Penninkx, S. Saurabh, and D. M. Thilikos. (meta) kernelization. In Foundations of Computer Science, FOCS 2009, pages 629-638. IEEE Computer Society, 2009. Google Scholar
  4. M. Cygan, F. V. Fomin, L. Kowalik, D. Lokshtanov, D. Marx, M. Pilipczuk, M. Pilipczuk, and S. Saurabh. Parameterized Algorithms. Springer, 2015. Google Scholar
  5. E. D. Demaine, F. V. Fomin, M. T. Hajiaghayi, and D. M. Thilikos. Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs. J. ACM, 52(6):866-893, 2005. Google Scholar
  6. E. D. Demaine and M. T. Hajiaghayi. The bidimensionality theory and its algorithmic applications. Comput. J., 51(3):292-302, 2008. Google Scholar
  7. R. G. Downey and M. R. Fellows. Fundamentals of Parameterized Complexity. Springer, 2013. Google Scholar
  8. F. V. Fomin, D. Lokshtanov, N. Misra, G. Philip, and S. Saurabh. Hitting forbidden minors: Approximation and kernelization. In Symposium on Theoretical Aspects of Computer Science, STACS 2011, volume 9 of LIPIcs, pages 189-200. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2011. Google Scholar
  9. G. Gutin and M. Jones. Parameterized algorithms for load coloring problem. Inf. Process. Lett., 114(8):446-449, 2014. Google Scholar
  10. S. Kratsch. Recent developments in kernelization: A survey. Bulletin of the EATCS, 113, 2014. Google Scholar
  11. D. Lokshtanov, N. Misra, and S. Saurabh. Kernelization - preprocessing with a guarantee. In The Multivariate Algorithmic Revolution and Beyond, volume 7370 of Lecture Notes in Computer Science, pages 129-161. Springer, 2012. Google Scholar
  12. E. Prieto. The method of extremal structure on the k-maximum cut problem. In Theory of Computing 2005, Eleventh CATS 2005, Computing: The Australasian Theory Symposium, Newcastle, NSW, Australia, January/February 2005, volume 41 of CRPIT, pages 119-126. Australian Computer Society, 2005. Google Scholar
  13. J. Shallit, 2002. URL: http://oeis.org/A073121.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail