Advertisement

Minimum Eccentricity Shortest Paths in Some Structured Graph Classes

  • Feodor F. Dragan
  • Arne LeitertEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9224)

Abstract

We investigate the Minimum Eccentricity Shortest Path problem in some structured graph classes. It asks for a given graph to find a shortest path with minimum eccentricity. Although it is NP-hard in general graphs, we demonstrate that a minimum eccentricity shortest path can be found in linear time for distance-hereditary graphs (generalizing the previous result for trees) and in \(\mathcal {O}(n^3m)\) time for chordal graphs.

Keywords

Short Path Linear Time General Graph Chordal Graph Graph Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgement

This work was partially supported by the NIH grant R01 GM103309.

References

  1. 1.
    Bandelt, H.-J., Mulder, H.M.: Distance-hereditary graphs. J. Comb. Theor. Ser. B 41, 182–208 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Brandstädt, A., Le, V.B., Spinrad, J.: Graph Classes: A Survey. SIAM, Philadelphia (1999)CrossRefzbMATHGoogle Scholar
  3. 3.
    Chang, G.J., Nemhauser, G.L.: The k-domination and k-stability problems on sun-free chordal graphs. SIAM J. Algebraic Discrete Meth. 5, 332–345 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Corneil, D.G., Olariu, S., Stewart, L.: Linear time algorithms for dominating pairs in asteroidal triple-free graphs. SIAM J. Comput. 28, 292–302 (1997)MathSciNetzbMATHGoogle Scholar
  5. 5.
    D’Atri, A., Moscarini, M.: Distance-hereditaxy graphs, Steiner trees and connected domination. SIAM J. Comput. 17, 521–538 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Dragan, F.F., Köhler, E., Leitert, A.: Line-distortion, bandwidth and path-length of a graph. In: Ravi, R., Gørtz, I.L. (eds.) SWAT 2014. LNCS, vol. 8503, pp. 158–169. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  7. 7.
    Dragan, F.F., Leitert, A.: On the minimum eccentricity shortest path problem. In: Dehne, F., Sack, J.-R., Stege, U. (eds.) WADS 2015. LNCS, vol. 9214, pp. 276–288. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  8. 8.
    Dragan, F.F., Nicolai, F.: LexBFS-orderings of distance-hereditary graphs with application to the diametral pair problem. Discrete Appl. Math. 98, 191–207 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Faber, M., Jamison, R.E.: Convexity in graphs and hypergraphs. SIAM J. Algebraic Discrete Methods 7, 433–444 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Howorka, E.: A characterization of distance-hereditary graphs. Quart. J. Math. Oxford Ser. 2(28), 417–420 (1977)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Lichtenstein, D.: Planar formulae and their uses. SIAM J. Comput. 11, 329–343 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Müller, H.: Hamiltonian circuits in chordal bipartite graphs. Discrete Math. 156, 291–298 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Slater, P.J.: Locating central paths in a graph. Transp. Sci. 16, 1–18 (1982)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Computer ScienceKent State UniversityKentUSA

Personalised recommendations