Abstract
The Bipartite Contraction problem is to decide, given a graph G and a parameter k, whether we can can obtain a bipartite graph from G by at most k edge contractions. The fixed-parameter tractability of the problem was shown by Heggernes et al. [13], with an algorithm whose running time has double-exponential dependence on k. We present a new randomized FPT algorithm for the problem, which is both conceptually simpler and achieves an improved \(2^{O(k^2)} n m\) running time, i.e., avoiding the double-exponential dependence on k. The algorithm can be derandomized using standard techniques.
Research supported by the European Research Council (ERC) grant “PARAMTIGHT: Parameterized complexity and the search for tight complexity results,” reference 280152 and OTKA grant NK105645.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alon, N., Yuster, R., Zwick, U.: Color-coding. J. ACM 42(4), 844–856 (1995)
Cao, Y., Marx, D.: Interval deletion is fixed-parameter tractable. CoRR, abs/1211.5933 (2012), Accepted to SODA 2014
Chen, J., Fomin, F.V., Liu, Y., Lu, S., Villanger, Y.: Improved algorithms for feedback vertex set problems. J. Comput. Syst. Sci. 74(7), 1188–1198 (2008)
Chen, J., Liu, Y., Lu, S.: An improved parameterized algorithm for the minimum node multiway cut problem. Algorithmica 55(1), 1–13 (2009)
Chen, J., Liu, Y., Lu, S., O’Sullivan, B., Razgon, I.: A fixed-parameter algorithm for the directed feedback vertex set problem. J. ACM 55(5) (2008)
Chitnis, R.H., Hajiaghayi, M., Marx, D.: Fixed-parameter tractability of directed multiway cut parameterized by the size of the cutset. SIAM Journal of Computing 42(4), 1674–1696 (2013), http://arxiv.org/abs/1110.0259
Cygan, M., Pilipczuk, M., Pilipczuk, M.: On Group Feedback Vertex Set Parameterized by the Size of the Cutset. In: Golumbic, M.C., Stern, M., Levy, A., Morgenstern, G. (eds.) WG 2012. LNCS, vol. 7551, pp. 194–205. Springer, Heidelberg (2012)
Dehne, F.K., Fellows, M.R., Langston, M.A., Rosamond, F.A., Stevens, K.: An O(2O(k) n 3) FPT algorithm for the undirected feedback vertex set problem. Theor. Comput. Syst. 41(3), 479–492 (2007)
Golovach, P.A., van ’t Hof, P., Paulusma, D.: Obtaining Planarity by Contracting Few Edges. In: Rovan, B., Sassone, V., Widmayer, P. (eds.) MFCS 2012. LNCS, vol. 7464, pp. 455–466. Springer, Heidelberg (2012)
Guillemot, S.: FPT algorithms for path-transversals and cycle-transversals problems. Discrete Optimization 8(1), 61–71 (2011)
Guo, J., Gramm, J., Hüffner, F., Niedermeier, R., Wernicke, S.: Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization. J. Comput. Syst. Sci. 72(8), 1386–1396 (2006)
Heggernes, P., van ’t Hof, P., Lévêque, B., Lokshtanov, D., Paul, C.: Contracting Graphs to Paths and Trees. In: Marx, D., Rossmanith, P. (eds.) IPEC 2011. LNCS, vol. 7112, pp. 55–66. Springer, Heidelberg (2012)
Heggernes, P., van’t Hof, P., Lokshtanov, D., Paul, C.: Obtaining a Bipartite Graph by Contracting Few Edges. In: FSTTCS 2011, pp. 217–228 (2011)
Iwata, Y., Oka, K., Yoshida, Y.: Linear-time FPT algorithms via network flow. CoRR, abs/1307.4927 (2013), Accepted to SODA 2014
Kawarabayashi, K., Reed, B.A.: An (almost) Linear Time Algorithm for Odd Cycle Transversal. In: SODA 2010, pp. 365–378 (2010)
Kratsch, S., Wahlström, M.: Compression via Matroids: a Randomized Polynomial Kernel for Odd Cycle Transversal. In: SODA 2012, pp. 94–103 (2012)
Kratsch, S., Wahlström, M.: Representative sets and irrelevant vertices: New tools for kernelization. In: FOCS 2012, pp. 450–459 (2012)
Lokshtanov, D., Saurabh, S., Sikdar, S.: Simpler Parameterized Algorithm for OCT. In: Fiala, J., Kratochvíl, J., Miller, M. (eds.) IWOCA 2009. LNCS, vol. 5874, pp. 380–384. Springer, Heidelberg (2009)
Marx, D.: Parameterized graph separation problems. Theoretical Computer Science 351(3), 394–406 (2006)
Marx, D.: Chordal deletion is fixed-parameter tractable. Algorithmica 57(4), 747–768 (2010)
Marx, D., O’Sullivan, B., Razgon, I.: Finding small separators in linear time via treewidth reduction. ACM Transactions on Algorithms 9(4) (2013)
Marx, D., Schlotter, I.: Obtaining a planar graph by vertex deletion. Algorithmica 62(3–4), 807–822 (2012)
Naor, M., Schulman, L.J., Srinivasan, A.: Splitters and near-optimal derandomization. In: FOCS 1995, pp. 182–191 (1995)
Narayanaswamy, N., Raman, V., Ramanujan, M., Saurabh, S.: LP can be a cure for Parameterized Problems. In: STACS 2012, pp. 338–349 (2012)
Ramanujan, M.S., Saurabh, S.: Linear time parameterized algorithms via skew-symmetric multicuts. CoRR, abs/1304.7505 (2013), Accepted to SODA 2014
Reed, B.A., Smith, K., Vetta, A.: Finding odd cycle transversals. Oper. Res. Lett. 32(4), 299–301 (2004)
Villanger, Y., Heggernes, P., Paul, C., Telle, J.A.: Interval completion is fixed parameter tractable. SIAM J. Comput. 38(5), 2007–2020 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this paper
Cite this paper
Guillemot, S., Marx, D. (2013). A Faster FPT Algorithm for Bipartite Contraction. In: Gutin, G., Szeider, S. (eds) Parameterized and Exact Computation. IPEC 2013. Lecture Notes in Computer Science, vol 8246. Springer, Cham. https://doi.org/10.1007/978-3-319-03898-8_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-03898-8_16
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03897-1
Online ISBN: 978-3-319-03898-8
eBook Packages: Computer ScienceComputer Science (R0)