Finding cores of limited length

  • Stephen Alstrup
  • Peter W. Lauridsen
  • Peer Sommerlund
  • Mikkel Thorup
Session 2B: Invited Lecture
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1272)


In this paper we consider the problem of finding a core of limited length in a tree. A core is a path, which minimizes the sum of the distances to all nodes in the tree. This problem has been examined under different constraints on the tree and on the set of paths, from which the core can be chosen. For all cases, we present linear or almost linear time algorithms, which improves the previous results due to Lo and Peng, J. Algorithms Vol. 20, 1996 and Minieka, Networks Vol. 15, 1985.


Piecewise Linear Function Leaf Tree Linear Time Algorithm Lower Envelope Core Problem 
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.


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  1. 1.
    S. Alstrup, P.W. Lauridsen, P. Sommerlund, and M. Thorup. Finding cores of limited length. Technical report, Department of Computer Science, University of Copenhagen, 1997. See also stephen/newpapers.html.Google Scholar
  2. 2.
    H. Davenport and A. Schinzel. A combinatorial problem connected with differential equations. Amer. J. Math., 87:684–694, 1965.Google Scholar
  3. 3.
    A.J. Goldman. Optimal center location in simple networks. Transportation Sci., 5:212–221, 1971.Google Scholar
  4. 4.
    S.L. Hakimi, M. Labbé, and E.F. Schmeichel. On locating path-or tree-shaped facilities on networks. Networks, 23:543–555, 1993.Google Scholar
  5. 5.
    D. Harel and R.E. Tarjan. Fast algorithms for finding nearest common ancestors. Siam J. Comput, 13(2):338–355, 1984.Google Scholar
  6. 6.
    S. Hart and M. Sharir. Nonlinearity of davenport-schinzel sequences and of general path compression schemes. Combinatorica, 6:151–177, 1986.Google Scholar
  7. 7.
    W. Lo and S. Peng. An optimal parallel algorithm for a core of a tree. In International conference on Parallel processing, pages 326–329, 1992.Google Scholar
  8. 8.
    W. Lo and S. Peng. Efficient algorithms for finding a, core of a tree with a specified length. J. Algorithms, 20:445–458, 1996.Google Scholar
  9. 9.
    K. Mehlhorn. Data Structures and Algorithms 1: Sorting and Searching. EATCS. Springer, 1 edition, 1984.Google Scholar
  10. 10.
    E. Minieka. The optimal location of a path or tree in a tree network. Networks, 15:309–321, 1985.Google Scholar
  11. 11.
    E. Minieka and N.H. Patel. On finding the core of a tree with a specified length. J. Algorithms, 4:345–352, 1983.Google Scholar
  12. 12.
    C.A. Morgan and P.J. Slater. A linear algorithm for a core of a tree. J. Algorithms, 1:247–258, 1980.Google Scholar
  13. 13.
    S. Peng, A.B. Stephens, and Y. Yesha. Algorithms for a core and k-tree core of a tree. J. Algorithms, 15:143–159, 1993.Google Scholar
  14. 14.
    P.J. Slater. Locating central paths in a graph. Transportation Sci., 16:1–18, 1982.Google Scholar
  15. 15.
    A. Wiernik. Planar realizations of nonlinear davenport-schinzel sequences by segments. In Foundations of Computer Science, pages 97–106, 1986.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Stephen Alstrup
    • 1
  • Peter W. Lauridsen
    • 1
  • Peer Sommerlund
    • 1
  • Mikkel Thorup
    • 1
  1. 1.Department of Computer ScienceUniversity of CopenhagenDenmark

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