Document Open Access Logo

Multistage Vertex Cover

Authors Till Fluschnik , Rolf Niedermeier , Valentin Rohm, Philipp Zschoche



PDF
Thumbnail PDF

File

LIPIcs.IPEC.2019.14.pdf
  • Filesize: 0.57 MB
  • 14 pages

Document Identifiers

Author Details

Till Fluschnik
  • Algorithmics and Computational Complexity, Faculty IV, TU Berlin, Germany
Rolf Niedermeier
  • Algorithmics and Computational Complexity, Faculty IV, TU Berlin, Germany
Valentin Rohm
  • Algorithmics and Computational Complexity, Faculty IV, TU Berlin, Germany
Philipp Zschoche
  • Algorithmics and Computational Complexity, Faculty IV, TU Berlin, Germany

Cite AsGet BibTex

Till Fluschnik, Rolf Niedermeier, Valentin Rohm, and Philipp Zschoche. Multistage Vertex Cover. In 14th International Symposium on Parameterized and Exact Computation (IPEC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 148, pp. 14:1-14:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.IPEC.2019.14

Abstract

Covering all edges of a graph by a small number of vertices, this is the NP-hard Vertex Cover problem, is among the most fundamental algorithmic tasks. Following a recent trend in studying dynamic and temporal graphs, we initiate the study of Multistage Vertex Cover. Herein, having a series of graphs with same vertex set but over time changing edge sets (known as temporal graph consisting of time layers), the goal is to find for each layer of the temporal graph a small vertex cover and to guarantee that the two vertex cover sets between two subsequent layers differ not too much (specified by a given parameter). We show that, different from classic Vertex Cover and some other dynamic or temporal variants of it, Multistage Vertex Cover is computationally hard even in fairly restricted settings. On the positive side, however, we also spot several fixed-parameter tractability results based on some of the most natural parameterizations.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Mathematics of computing → Graph algorithms
Keywords
  • NP-hardness
  • dynamic graph problems
  • temporal graphs
  • time-evolving networks
  • W[1]-hardness
  • fixed-parameter tractability
  • kernelization

Metrics

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

References

  1. Faisal N. Abu-Khzam, Judith Egan, Michael R. Fellows, Frances A. Rosamond, and Peter Shaw. On the parameterized complexity of dynamic problems. Theor. Comput. Sci., 607:426-434, 2015. Google Scholar
  2. Eleni C. Akrida, George B. Mertzios, Paul G. Spirakis, and Viktor Zamaraev. Temporal Vertex Cover with a Sliding Time Window. In Proc. of 45th ICALP, volume 107 of LIPIcs, pages 148:1-148:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. Google Scholar
  3. Josh Alman, Matthias Mnich, and Virginia Vassilevska Williams. Dynamic Parameterized Problems and Algorithms. In Proc. of 44th ICALP, volume 80 of LIPIcs, pages 41:1-41:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. Google Scholar
  4. Evripidis Bampis, Bruno Escoffier, Michael Lampis, and Vangelis Th. Paschos. Multistage Matchings. In Proc. of 16th SWAT, volume 101 of LIPIcs, pages 7:1-7:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. Google Scholar
  5. Evripidis Bampis, Bruno Escoffier, and Alexandre Teiller. Multistage Knapsack. In Proc. of 44th MFCS, volume 138 of LIPIcs, pages 22:1-22:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. Google Scholar
  6. Rajesh Chitnis, Graham Cormode, Hossein Esfandiari, MohammadTaghi Hajiaghayi, Andrew McGregor, Morteza Monemizadeh, and Sofya Vorotnikova. Kernelization via Sampling with Applications to Finding Matchings and Related Problems in Dynamic Graph Streams. In Proc. of 27th SODA, pages 1326-1344. SIAM, 2016. Google Scholar
  7. Marek Cygan, Fedor V Fomin, Łukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michał Pilipczuk, and Saket Saurabh. Parameterized Algorithms. Springer, 2015. Google Scholar
  8. Reinhard Diestel. Graph Theory, volume 173 of GTM. Springer, 5th edition, 2016. Google Scholar
  9. Rodney G. Downey and Michael R. Fellows. Parameterized Complexity. Monographs in Computer Science. Springer, 1999. Google Scholar
  10. Andrew Drucker. New Limits to Classical and Quantum Instance Compression. SIAM J. Comput., 44(5):1443-1479, 2015. Google Scholar
  11. David Eisenstat, Claire Mathieu, and Nicolas Schabanel. Facility Location in Evolving Metrics. In Proc. of 41st ICALP, volume 8573 of LNCS, pages 459-470. Springer, 2014. Google Scholar
  12. Herbert Fleischner, Gert Sabidussi, and Vladimir I. Sarvanov. Maximum independent sets in 3- and 4-regular Hamiltonian graphs. Discrete Math., 310(20):2742-2749, 2010. Google Scholar
  13. Till Fluschnik, Hendrik Molter, Rolf Niedermeier, Malte Renken, and Philipp Zschoche. Temporal Graph Classes: A View Through Temporal Separators. Theor. Comput. Sci., 2019. In press. Google Scholar
  14. M. R. Garey, David S. Johnson, and Larry J. Stockmeyer. Some Simplified NP-Complete Graph Problems. Theor. Comput. Sci., 1(3):237-267, 1976. Google Scholar
  15. Parikshit Gopalan, Phokion G Kolaitis, Elitza Maneva, and Christos H Papadimitriou. The connectivity of Boolean satisfiability: computational and structural dichotomies. SIAM J. Comput., 38(6):2330-2355, 2009. Google Scholar
  16. Anupam Gupta, Kunal Talwar, and Udi Wieder. Changing Bases: Multistage Optimization for Matroids and Matchings. In Proc. of 41st ICALP, volume 8572 of LNCS, pages 563-575. Springer, 2014. Google Scholar
  17. Sepp Hartung and Rolf Niedermeier. Incremental list coloring of graphs, parameterized by conservation. Theor. Comput. Sci., 494:86-98, 2013. Google Scholar
  18. Takehiro Ito, Erik D Demaine, Nicholas JA Harvey, Christos H Papadimitriou, Martha Sideri, Ryuhei Uehara, and Yushi Uno. On the complexity of reconfiguration problems. Theor. Comput. Sci., 412(12-14):1054-1065, 2011. Google Scholar
  19. Yoichi Iwata and Keigo Oka. Fast Dynamic Graph Algorithms for Parameterized Problems. In Proc. of 12th SWAT, volume 8503 of LNCS, pages 241-252. Springer, 2014. Google Scholar
  20. R. Krithika, Abhishek Sahu, and Prafullkumar Tale. Dynamic Parameterized Problems. Algorithmica, 80(9):2637-2655, 2018. Google Scholar
  21. Amer Mouawad, Naomi Nishimura, Venkatesh Raman, and Sebastian Siebertz. Vertex cover reconfiguration and beyond. Algorithms, 11(2):20, 2018. Google Scholar
  22. Amer E Mouawad, Naomi Nishimura, Venkatesh Raman, Narges Simjour, and Akira Suzuki. On the parameterized complexity of reconfiguration problems. Algorithmica, 78(1):274-297, 2017. Google Scholar
  23. Chee-Keng Yap. Some Consequences of Non-Uniform Conditions on Uniform Classes. Theor. Comput. Sci., 26:287-300, 1983. Google Scholar
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