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An effective branching strategy based on structural relationship among multiple forbidden induced subgraphs

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Abstract

Branching on forbidden induced subgraphs is a genetic strategy to obtain parameterized algorithms for many edge modification problems. For such a problem in which the graph property is defined by multiple forbidden induced subgraphs, branching process is trivially performed on each subgraph. Thus, the size of the resulting search tree is dominated by the size of the largest forbidden subgraph. In this paper, we present a simple strategy for deriving significantly improved branching rules to deal with multiple forbidden subgraphs by edge modifications. The basic idea hereby is that while constructing branching rules for the largest forbidden subgraph, we sufficiently take into account the structural relationship between it and other forbidden subgraphs. By applying this strategy, we obtain improved parameterized algorithms for edge modification problems for several graph properties such as 3-leaf power, proper interval, threshold and co-trivially perfect graphs.

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Notes

  1. This result was claimed in author’s conference presentation (Villanger 2010a) and the vertex deletion of the problem is fixed-parameter tractable (Villanger 2010b).

References

  • Bessy S, Paul C, Perez A (2010) Polynomial kernels for 3-leaf power graph modification problems. Discret Appl Math 158(16):1732–1744

    Article  MATH  MathSciNet  Google Scholar 

  • Bessy S, Perez A (2011) Polynomial kernels for proper interval completion and related problems. In: Proceedings of 18th international symposium on fundamentals of computer theory, vol 6914. Lecture Notes in Computer Science, pp 229–239

  • Brandstäda A, Le VB, Spinrad JP (1999) Graph classes: a survey (monographs on discrete mathematics and applications). SIAM, Philadelphia

    Book  Google Scholar 

  • Cai L (1996) Fixed-parameter tractability of graph modification problems for hereditary properties. Inf Process Lett 58(4):171–196

    Article  MATH  Google Scholar 

  • Downey R, Fellows M (1999) Parameterized complexity. Springer-Verlag, Berlin

    Book  Google Scholar 

  • Dom M, Guo J, Hüffner F, Niedermeier R (2006) Error compensation in leaf power problems. Algorithmica 44(4):363–381

    Article  MATH  MathSciNet  Google Scholar 

  • Feng Q, Wang J, Chen J (2014) Matching and weighted P2-packing: algorithms and kernels. Theor Comput Sci 522:85–94

    Google Scholar 

  • Gramm J, Guo J, Hüffner F, Niedermeier R (2004) Automated generation of search tree algorithms for hard graph modification problems. Algorithmica 39(4):321–347

    Article  MATH  MathSciNet  Google Scholar 

  • Guo J, Hüffner F, Komusiewicz C, Zhang Y (2008) Improved algorithms for bicluster editing. In: Proceedings of 5th theory and applications of models of computation, vol 4978. Lecture Notes in Computer Science, pp 445–456

  • Guo J (2007) Problem kernels for NP-complete edge modification problems: split and related graphs. In: Proceedings of 18th international symposium on algorithms and computation, vol 4835. Lecture Notes in Computer Science, pp 915–926

  • Kaplan H, Shamir R, Tarjan RE (1999) Tractability of parameterized completion problems on chordal, strongly chordal, and proper interval graphs. SIAM J. Comput. 28(5):1906–1922

    Article  MATH  MathSciNet  Google Scholar 

  • Liu Y, Wang J, Guo J, Chen J (2012) Complexity and parameterized algorithms for cograph editing. Theor Comput Sci 461:45–54

    Article  MATH  MathSciNet  Google Scholar 

  • Nastos J, Gao Y (2010) A novel branching strategy for parameterized graph modification problems. In: Proceedings of 4th annual international conference on combinatorial optimization and applications, vol 6509. Lecture Notes in Computer Science, pp 332–346

  • Niedermeier R, Rossmanith P (2000) A general method to speed up fixed-parameter tractable algorithms. Inf Process Lett 73:125–129

    Article  MATH  MathSciNet  Google Scholar 

  • Sharan R (2002) Graph modification problems and their applications to genomic research. PhD thesis, Tel-Aviv University

  • Villanger Y (2010a) Proper interval vertex deletion. Presentation in the 5th international symposium on parameterized and exact computation. http://www.lirmm.fr/~paul/ANR/CIRM-TALKS-2010/Villanger-cirm-2010.pdf

  • Villanger Y (2010b) Proper interval vertex deletion. In: Proceedings of the 5th international symposium on parameterized and exact computation, vol 6478. Lecture Notes in Computer Science, pp 228–238

  • Wang J, Tan P, Yao J, Feng Q, Chen J (2013) On the minimum link-length rectilinear spanning path problem: complexity and algorithms. IEEE Trans Comput. doi:10.1109/TC.2013.163

  • Wegner G (1967) Eigenschaften der Nerven homologisch-einfacher Familien im \(R^{n}\). PhD thesis, Universität Göttingen

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Authors and Affiliations

  1. School of Information Science and Engineering, Central South University, Changsha , 410083, People’s Republic of China

    Yunlong Liu, Jianxin Wang, Chao Xu & Jianer Chen

  2. College of Mathematics and Computer Science, Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China), Hunan Normal University, Changsha , 410081, People’s Republic of China

    Yunlong Liu

  3. Universität des Saarlandes, Campus E 1.7, 66123, Saarbrücken , Germany

    Jiong Guo

  4. Department of Computer Science, Texas A&M University, College Station, TX, USA

    Jianer Chen

Authors
  1. Yunlong Liu
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  2. Jianxin Wang
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  3. Chao Xu
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  4. Jiong Guo
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  5. Jianer Chen
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Corresponding author

Correspondence to Jianxin Wang.

Additional information

A preliminary version of this paper was presented at the 19th Annual International Computing and Combinatorics Conference (COCOON 2013), June 21–23, 2013, Hangzhou, China. This research was supported in part by the National Natural Science Foundation of China under Grant Nos. 61070224, 61232001, and 61173051, the China Postdoctoral Science Foundation funded project under Grant No. 2012M521551, and the DFG Cluster of Excellence “Multimodal Computing and Interaction (MMCI)”.

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Liu, Y., Wang, J., Xu, C. et al. An effective branching strategy based on structural relationship among multiple forbidden induced subgraphs. J Comb Optim 29, 257–275 (2015). https://doi.org/10.1007/s10878-014-9733-1

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  • DOI: https://doi.org/10.1007/s10878-014-9733-1

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