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Non-greedy Online Steiner Trees on Outerplanar Graphs

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Approximation and Online Algorithms (WAOA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10138))

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Abstract

This paper addresses the classical online Steiner tree problem on edge-weighted graphs. It is known that a greedy (nearest neighbor) online algorithm has a tight competitive ratio for wide classes of graphs, such as trees, rings, any class including series-parallel graphs, and unweighted graphs with bounded diameter. However, we did not know any greedy or non-greedy tight deterministic algorithm for other classes of graphs. In this paper, we observe that a greedy algorithm is \(\varOmega (\log n)\)-competitive on outerplanar graphs, where n is the number of vertices, and propose a 5.828-competitive deterministic algorithm on outerplanar graphs. Our algorithm connects a requested vertex and the tree constructed thus far using a path that is constant times longer than the distance between them. The algorithm can be applied to a 21.752-competitive file allocation algorithm against adaptive online adversaries on outerplanar graphs. We also present a lower bound of 4 for arbitrary deterministic online Steiner tree algorithms on outerplanar graphs.

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References

  1. Alon, N., Azar, Y.: On-line steiner trees in the Euclidean plane. Discret. Comput. Geom. 10, 113–121 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  2. Angelopoulos, S.: Online priority steiner tree problems. In: Dehne, F., Gavrilova, M., Sack, J.-R., Tóth, C.D. (eds.) WADS 2009. LNCS, vol. 5664, pp. 37–48. Springer, Heidelberg (2009). doi:10.1007/978-3-642-03367-4_4

    Chapter  Google Scholar 

  3. Angelopoulos, S.: Parameterized analysis of online steiner tree problems. In: Adaptive, Output Sensitive, Online and Parameterized Algorithms. Dagstuhl Seminar Proceedings (2009). http://drops.dagstuhl.de/opus/volltexte/2009/2121

  4. Angelopoulos, S.: On the competitiveness of the online asymmetric and Euclidean steiner tree problems. In: Bampis, E., Jansen, K. (eds.) WAOA 2009. LNCS, vol. 5893, pp. 1–12. Springer, Heidelberg (2010). doi:10.1007/978-3-642-12450-1_1

    Chapter  Google Scholar 

  5. Averbuch, B., Azar, Y., Bartal, Y.: On-line generalized steiner problem. Theor. Comput. Sci. 324, 313–324 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  6. Awerbuch, B., Bartal, Y., Fiat, A.: Competitive distributed file allocation. Inf. Comput. 185(1), 1–40 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Bartal, Y., Fiat, A., Rabani, Y.: Competitive algorithms for distributed data management. J. Comput. Syst. Sci. 51(3), 341–358 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  8. Berman, P., Coulston, C.: On-line algorithms for steiner tree problems. In: Proceedings of the 29th ACM Symposium on Theory of Computing, pp. 344–353 (1997)

    Google Scholar 

  9. Chekuri, C., Gupta, A., Newman, I., Rabinovich, Y., Sinclair, A.: Embedding \(k\)-outerplanar graphs into \(\ell _1\). SIAM J. Discret. Math. 20(1), 119–136 (2006)

    Article  MATH  Google Scholar 

  10. Fleischner, H.J., Geller, D.P., Harary, F.: Outerplanar graphs and weak duals. J. Indian Math. Soc. 38, 215–219 (1974)

    MATH  MathSciNet  Google Scholar 

  11. Gupta, A., Newman, I., Rabinovich, Y., Sinclair, A.: Cuts, trees, and \(\ell _1\)-embedding of graphs. Combinatorica 24(2), 233–269 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  12. Imase, M., Waxman, B.M.: Dynamic steiner tree problem. SIAM J. Discret. Math. 4(3), 369–384 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  13. Lund, C., Reingold, N., Westbrook, J., Yan, D.: Competitive on-line algorithms for distributed data management. SIAM J. Comput. 28(3), 1086–1111 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  14. Naor, J.S., Panigrahi, D., Singh, M.: Online node-weighted steiner tree and related problems. In: Proceedings 52nd Annual IEEE Symposium on Foundations of Computer Science, pp. 210–219 (2011)

    Google Scholar 

  15. Westbrook, J., Yan, D.C.K.: The performance of greedy algorithms for the on-line steiner tree and related problems. Math. Syst. Theory 28, 451–468 (1995)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Division of Electrical Engineering and Computer Science, Kanazawa University, Kanazawa, 920-1192, Japan

    Akira Matsubayashi

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  1. Akira Matsubayashi
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Correspondence to Akira Matsubayashi .

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Editors and Affiliations

  1. Institut für Informatik, Christian-Albrechts-Universität, Kiel, Germany

    Klaus Jansen

  2. Istituto Dalle Molle di Studi sull’ Intelligenza Artificiale, Manno (Lugano), Switzerland

    Monaldo Mastrolilli

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Matsubayashi, A. (2017). Non-greedy Online Steiner Trees on Outerplanar Graphs. In: Jansen, K., Mastrolilli, M. (eds) Approximation and Online Algorithms. WAOA 2016. Lecture Notes in Computer Science(), vol 10138. Springer, Cham. https://doi.org/10.1007/978-3-319-51741-4_11

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  • DOI: https://doi.org/10.1007/978-3-319-51741-4_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-51740-7

  • Online ISBN: 978-3-319-51741-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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