Abstract
The quest for colorful components (connected components where each color is associated with at most one vertex) inside a vertex-colored graph has been widely considered in the last ten years. Here we consider two variants, Minimum Colorful Components (MCC) and Maximum Edges in transitive Closure (MEC), introduced in the context of orthology gene identification in bioinformatics. The input of both MCC and MEC is a vertex-colored graph. MCC asks for the removal of a subset of edges, so that the resulting graph is partitioned in the minimum number of colorful connected components; MEC asks for the removal of a subset of edges, so that the resulting graph is partitioned in colorful connected components and the number of edges in the transitive closure of such a graph is maximized. We study the parameterized and approximation complexity of MCC and MEC, for general and restricted instances.
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
Similar content being viewed by others
Notes
- 1.
The \(O^*\) notation suppresses polynomial factors.
References
Adamaszek, A., Blin, G., Popa, A.: Approximation and hardness results for the maximum edges in transitive closure problem. In: Jan, K., Miller, M., Froncek, D. (eds.) IWOCA 2014. LNCS, vol. 8986, pp. 13–23. Springer, Heidelberg (2015)
Adamaszek, A., Popa, A.: Algorithmic and hardness results for the colorful components problems. Algorithmica 73(2), 371–388 (2015)
Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.: Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties. Springer, Heidelberg (1999)
Betzler, N., van Bevern, R., Fellows, M.R., Komusiewicz, C., Niedermeier, R.: Parameterized algorithmics for finding connected motifs in biological networks. IEEE/ACM Trans. Comput. Biol. Bioinform. 8(5), 1296–1308 (2011)
Bruckner, S., Hüffner, F., Komusiewicz, C., Niedermeier, R., Thiel, S., Uhlmann, J.: Partitioning into colorful components by minimum edge deletions. In: Kärkkäinen, J., Stoye, J. (eds.) CPM 2012. LNCS, vol. 7354, pp. 56–69. Springer, Heidelberg (2012)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. MIT Press, Cambridge (2009)
Dondi, R., Fertin, G., Vialette, S.: Complexity issues in vertex-colored graph pattern matching. J. Discrete Algorithms 9(1), 82–99 (2011)
Dondi, R., Fertin, G., Vialette, S.: Finding approximate and constrained motifs in graphs. Theor. Comput. Sci. 483, 10–21 (2013)
Downey, R.G., Fellows, M.R.: Fundamentals of Parameterized Complexity. Springer, New York (2013)
Garg, N., Vazirani, V.V., Yannakakis, M.: Primal-dual approximation algorithms for integral flow and multicut in trees. Algorithmica 18(1), 3–20 (1997)
Komusiewicz, C., Niedermeier, R.: New races in parameterized algorithmics. In: Rovan, B., Sassone, V., Widmayer, P. (eds.) MFCS 2012. LNCS, vol. 7464, pp. 19–30. Springer, Heidelberg (2012)
Lacroix, V., Fernandes, C.G., Sagot, M.: Motif search in graphs: application to metabolic networks. IEEE/ACM Trans. Comput. Biol. Bioinform. 3(4), 360–368 (2006)
Zheng, C., Swenson, K., Lyons, E., Sankoff, D.: OMG! Orthologs in multiple genomes – competing graph-theoretical formulations. In: Przytycka, T.M., Sagot, M.-F. (eds.) WABI 2011. LNCS, vol. 6833, pp. 364–375. Springer, Heidelberg (2011)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Dondi, R., Sikora, F. (2016). Parameterized Complexity and Approximation Issues for the Colorful Components Problems. In: Beckmann, A., Bienvenu, L., Jonoska, N. (eds) Pursuit of the Universal. CiE 2016. Lecture Notes in Computer Science(), vol 9709. Springer, Cham. https://doi.org/10.1007/978-3-319-40189-8_27
Download citation
DOI: https://doi.org/10.1007/978-3-319-40189-8_27
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-40188-1
Online ISBN: 978-3-319-40189-8
eBook Packages: Computer ScienceComputer Science (R0)