Carrying Umbrellas: An Online Relocation Problem on Graphs

  • Jae-Ha Lee
  • Chong-Dae Park
  • Kyung-Yong Chwa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1741)


We introduce an online relocation problem on a graph, in which a player who walks around the nodes makes decisions on whether to relocate mobile resources, while not knowing the future requests. We call it Carrying Umbrellas. This paper gives a necessary and sufficient condition under which a competitive algorithm exists and describes an optimal algorithm and anaylzes its competitve ratio. We also extend this problem to the case of digraphs.


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  1. 1.
    N. Alon, R. M. Karp, D. Peleg, and D. West. A graph-theoretic game and its application to the k-server problem. SIAM J. of Comput., 24(1):78–100, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    R. Beigel and W.I Gasarch. The mapmaker’s dilemma. Discrete Applied Mathematics, 34(1):37–48, 1991.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Ben-David, A. Borodin, R.M. Karp, G. Tardos, and A. Widgerson. On the power of randomization in online algorithms. In Proc. of 22nd STOC, pages 379–386, 1990.Google Scholar
  4. 4.
    Hans L. Bodlaender. On the complexity of some coloring games. Int. J. of Foundation of Computer Science, 2:133–147, 1991.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    A. Borodin and R. El-Yaniv. Online computation and competitive analysis. Cambridge University Press, 1998.Google Scholar
  6. 6.
    M. Chrobak and L. Larmore. The searver problem and online game. In DIMACS Series in Discrete Mathematics and Theoretical Computer Science, volume 7, pages 11–64. AMS-ACM, 1992.MathSciNetGoogle Scholar
  7. 7.
    P. Raghavan and M. Snir. Memory versus randomization in online algorithms. In Proc. of 16th ICALP, pages 687–703, 1987.Google Scholar
  8. 8.
    D. Sleator and R. Tarjan. Amortized efficiency of list update and paging rules. Communications of ACM, 2(28):202–208, 1985.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Jae-Ha Lee
    • 1
  • Chong-Dae Park
    • 1
  • Kyung-Yong Chwa
    • 1
  1. 1.Dept. of Computer ScienceKAISTKorea

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