Skip to main content

Advertisement

SpringerLink
Log in

A graph theoretical approach for node covering in tree based architectures and its application to bioinformatics

  • Original Article
  • Published:
Network Modeling Analysis in Health Informatics and Bioinformatics Aims and scope Submit manuscript

Abstract

Investigation of DNA sequences is a paramount stage for apprehending biological structures and functions. The known methods for investigating DNA sequence alignments usually fail to produce an exact solution. Motivated by the problem of finding similarities in DNA and amino sequences, we study certain classes of phylogenetic trees and present an exact solution for the minimum node cover which can be used for genetic sequence comparisons. The smallest number of nodes removed to disconnect a graph \(G\) is the smallest node cover. In this paper, we address the problem of finding a minimum node cover for certain tree-derived architectures, namely, Hyper trees, Slim trees, \(X\) trees, \(l\)-sibling trees, and \(k\)-rooted sibling trees. Trees are advantageous in biology especially for bioinformatics, systematics, and phylogenetics. The smallest node cover set is the minimum number of nodes in a graph which monitors all the edges in the graph. Therefore, these sets are much useful in bioinformatics workflow management system. Moreover, our results can also be applied to identify genetic variants and to characterize common DNA variants.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Alimonti P, Kann V (2000) Some APX-completeness results for cubic graphs. Theor Comput Sci 237(1):123–134

    Article  MathSciNet  Google Scholar 

  • Auyeung A, Abraham A (2004) The largest compatible subset problem for phylogenetic data, genetic and evolutionary computation 2004 conference (GECCO-2004), bird-of-a-feather workshop on application of hybrid evolutionary algorithms to complex optimization problems. Springer, Berlin, pp 1–11

    Google Scholar 

  • Babar ME, Pervez MT, Nadeem A, Hussain T, Aslam N (2014) Multiple sequence alignment tools: assessing performance of the underlying algorithms. J Appl Environ Biol Sci 4(8S):76–80

    Google Scholar 

  • Chen J, Kanj IA, Xia G (2010) Improved upper bounds for vertex cover. Theor Comput Sci 411:3736–3756

    Article  MathSciNet  Google Scholar 

  • Chen J, Lin Y, Li J, Lin G, Ma Z, Tan A (2016) A rough set method for the minimum vertex cover problem of graphs”. Appl Soft Comput 42:360–367

    Article  Google Scholar 

  • Corel E, Pitschi F, Morgenstern B (2010) A min-cut algorithm for the consistency problem in multiple sequence alignment. Bioinformatics 26(8):1015–1021. https://doi.org/10.1093/bioinformatics/btq082

    Article  Google Scholar 

  • Fernau H, Fomin FV, Philip G, Saurabh S (2015) On the parameterized complexity of vertex cover and edge cover with connectivity constraints. Theor Comput Sci 565:1–15

    Article  MathSciNet  Google Scholar 

  • Harary F (1993) Graph theory. Narosa Publishers, New Delhi, pp 21–23

    Google Scholar 

  • Hochbaum D (1983) Efficient bounds for the stable set, vertex cover and set packing problem. Discrete Appl Math 6(3):243–254

    Article  MathSciNet  Google Scholar 

  • Jianhua T (2015) A fixed-parameter algorithm for the vertex cover P3 problem. Inf Process Lett 115(2):96–99

    Article  Google Scholar 

  • Kamath SS, Bhat RS (2007) On strong (weak) independent sets and vertex coverings of a graph. Discrete Math 307(9–10):1136–1145

    Article  MathSciNet  Google Scholar 

  • Karakostas G (2005) A better approximation ratio for the vertex cover problem. In: Proceedings of the 32nd international colloquium, ICALP 2005, Lisbon, Portugal, July 11–15, pp 1043–1050

  • Karakostas G (2009) A better approximation ratio for the vertex cover problem. ACM Trans Algorithms 5(4):1–8

    Article  MathSciNet  Google Scholar 

  • Karp RM (1972) Reducibility among combinatorial problems, complexity of computer computations. Springer, Berlin, pp 85–103

    Book  Google Scholar 

  • Paul D, Rajasingh I, Rajan RS (2015) Tree derived architectures with decycling number equal to cycle packing number. Procedia Comput Sci 57:716–726

    Article  Google Scholar 

  • Wang Z, Huang D, Tang C (2013) Fast parallel algorithm to the minimum edge cover problem based on DNA molecular computation. Appl Math Inf Sci 7(2):711–716

    Article  MathSciNet  Google Scholar 

  • Xu H, Kumar TS, Koenig S (2016) A new solver for the minimum weighted vertex cover problem, integration of AI and OR techniques in constraint programming, lecture notes in computer science, vol 9676, pp 392–405

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Sathyabama Institute of Science and Technology, Chennai, 600119, India

    D. Angel

Authors
  1. D. Angel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. Angel.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

D., A. A graph theoretical approach for node covering in tree based architectures and its application to bioinformatics. Netw Model Anal Health Inform Bioinforma 8, 12 (2019). https://doi.org/10.1007/s13721-019-0193-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s13721-019-0193-5

Keywords

Search

Navigation