Abstract
We study a family of problems where the goal is to make a graph Eulerian by a minimum number of deletions. We completely classify the parameterized complexity of various versions: undirected or directed graphs, vertex or edge deletions, with or without the requirement of connectivity, etc. Of particular interest is a randomized FPT algorithm for making an undirected graph Eulerian by deleting the minimum number of edges.
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
Ahuja, R.K., Goldberg, A.V., Orlin, J.B., Tarjan, R.E.: Finding minimum-cost flows by double scaling. Math. Program. 53, 243–266 (1992)
Alon, N., Shapira, A., Sudakov, B.: Additive approximation for edge-deletion problems. In: FOCS, pp. 419–428 (2005)
Alon, N., Yuster, R., Zwick, U.: Color-coding. J. ACM 42(4), 844–856 (1995)
van Bevern, R., Moser, H., Niedermeier, R.: Approximation and tidying—a problem kernel for s-plex cluster vertex deletion. Algorithmica (February 2011)
Bodlaender, H.L., Jansen, B.M.P., Kratsch, S.: Cross-composition: A new technique for kernelization lower bounds. CoRR abs/1011.4224 (2010)
Burzyn, P., Bonomo, F., Durán, G.: NP-completeness results for edge modification problems. Discrete Appl. Math. 154, 1824–1844 (2006)
Cai, J., Chakaravarthy, V.T., Hemaspaandra, L.A., Ogihara, M.: Competing provers yield improved Karp-Lipton collapse results. Inf. Comput. 198(1), 1–23 (2005)
Cai, L.: Fixed-parameter tractability of graph modification problems for hereditary properties. Inf. Process. Lett. 58(4), 171–176 (1996)
Cai, L., Yang, B.: Parameterized Complexity of Even/Odd Subgraph Problems. In: Calamoneri, T., Diaz, J. (eds.) CIAC 2010. LNCS, vol. 6078, pp. 85–96. Springer, Heidelberg (2010)
Cechlárová, K., Schlotter, I.: Computing the Deficiency of Housing Markets with Duplicate Houses. In: Raman, V., Saurabh, S. (eds.) IPEC 2010. LNCS, vol. 6478, pp. 72–83. Springer, Heidelberg (2010)
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), 1–19 (2008)
Díaz, J., Thilikos, D.M.: Fast FPT-Algorithms for Cleaning Grids. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 361–371. Springer, Heidelberg (2006)
Dorn, F., Moser, H., Niedermeier, R., Weller, M.: Efficient Algorithms for Eulerian Extension. In: Thilikos, D.M. (ed.) WG 2010. LNCS, vol. 6410, pp. 100–111. Springer, Heidelberg (2010)
Edmonds, J., Johnson, E.: Matching, Euler tours and the Chinese postman problem. Math. Program. 5, 88–124 (1973)
Garey, M.R., Johnson, D.S., Tarjan, R.E.: The planar Hamiltonian circuit problem is NP-complete. SIAM J. on Computing 5, 704–714 (1976)
Guo, J.: Problem Kernels for NP-Complete Edge Deletion Problems: Split and Related Graphs. In: Tokuyama, T. (ed.) ISAAC 2007. LNCS, vol. 4835, pp. 915–926. Springer, Heidelberg (2007)
Khot, S., Raman, V.: Parameterized complexity of finding subgraphs with hereditary properties. Theor. Comput. Sci. 289, 997–1008 (2002)
Kolman, P., Pangrác, O.: On the complexity of paths avoiding forbidden pairs. Discrete Applied Mathematics 157(13), 2871–2876 (2009)
Kratsch, S., Wahlström, M.: Two Edge Modification Problems Without Polynomial Kernels. In: Chen, J., Fomin, F.V. (eds.) IWPEC 2009. LNCS, vol. 5917, pp. 264–275. Springer, Heidelberg (2009)
Lewis, J.M., Yannakakis, M.: The node-deletion problem for hereditary properties is NP-complete. J. Comput. Syst. Sci. 20(2), 219–230 (1980)
Lokshtanov, D.: Wheel-Free Deletion is W[2]-Hard. In: Grohe, M., Niedermeier, R. (eds.) IWPEC 2008. LNCS, vol. 5018, pp. 141–147. Springer, Heidelberg (2008)
Marx, D.: Chordal deletion is fixed-parameter tractable. Algorithmica 57(4), 747–768 (2010)
Mathieson, L., Szeider, S.: The parameterized complexity of regular subgraph problems and generalizations. In: CATS, pp. 79–86 (2008)
Moser, H., Thilikos, D.M.: Parameterized complexity of finding regular induced subgraphs. Journal of Discrete Algorithms 7, 181–190 (2009)
Natanzon, A., Shamir, R., Sharan, R.: Complexity classification of some edge modification problems. Discrete Appl. Math. 113, 109–128 (2001)
Philip, G., Raman, V., Villanger, Y.: A Quartic Kernel for Pathwidth-one Vertex Deletion. In: Thilikos, D.M. (ed.) WG 2010. LNCS, vol. 6410, pp. 196–207. Springer, Heidelberg (2010)
Plesník, J.: The NP-completeness of the Hamiltonian cycle problem in planar digraphs with degree bound two. Inf. Process. Lett. 8(4), 199–201 (1979)
Raman, V., Saurabh, S.: Parameterized algorithms for feedback set problems and their duals in tournaments. Theor. Comput. Sci. 351, 446–458 (2006)
Raman, V., Sikdar, S.: Parameterized complexity of the induced subgraph problem in directed graphs. Inf. Process. Lett. 104, 79–85 (2007)
Sorge, M.: On making directed graphs Eulerian. CoRR abs/1101.4283 (2011)
Yap, C.K.: Some consequences of non-uniform conditions on uniform classes. Theor. Comput. Sci. 26, 287–300 (1983)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cygan, M., Marx, D., Pilipczuk, M., Pilipczuk, M., Schlotter, I. (2011). Parameterized Complexity of Eulerian Deletion Problems. In: Kolman, P., Kratochvíl, J. (eds) Graph-Theoretic Concepts in Computer Science. WG 2011. Lecture Notes in Computer Science, vol 6986. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25870-1_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-25870-1_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25869-5
Online ISBN: 978-3-642-25870-1
eBook Packages: Computer ScienceComputer Science (R0)