Abstract
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.
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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 http://www.diku.dk/ stephen/newpapers.html.
H. Davenport and A. Schinzel. A combinatorial problem connected with differential equations. Amer. J. Math., 87:684–694, 1965.
A.J. Goldman. Optimal center location in simple networks. Transportation Sci., 5:212–221, 1971.
S.L. Hakimi, M. Labbé, and E.F. Schmeichel. On locating path-or tree-shaped facilities on networks. Networks, 23:543–555, 1993.
D. Harel and R.E. Tarjan. Fast algorithms for finding nearest common ancestors. Siam J. Comput, 13(2):338–355, 1984.
S. Hart and M. Sharir. Nonlinearity of davenport-schinzel sequences and of general path compression schemes. Combinatorica, 6:151–177, 1986.
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.
W. Lo and S. Peng. Efficient algorithms for finding a, core of a tree with a specified length. J. Algorithms, 20:445–458, 1996.
K. Mehlhorn. Data Structures and Algorithms 1: Sorting and Searching. EATCS. Springer, 1 edition, 1984.
E. Minieka. The optimal location of a path or tree in a tree network. Networks, 15:309–321, 1985.
E. Minieka and N.H. Patel. On finding the core of a tree with a specified length. J. Algorithms, 4:345–352, 1983.
C.A. Morgan and P.J. Slater. A linear algorithm for a core of a tree. J. Algorithms, 1:247–258, 1980.
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.
P.J. Slater. Locating central paths in a graph. Transportation Sci., 16:1–18, 1982.
A. Wiernik. Planar realizations of nonlinear davenport-schinzel sequences by segments. In Foundations of Computer Science, pages 97–106, 1986.
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© 1997 Springer-Verlag Berlin Heidelberg
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Alstrup, S., Lauridsen, P.W., Sommerlund, P., Thorup, M. (1997). Finding cores of limited length. In: Dehne, F., Rau-Chaplin, A., Sack, JR., Tamassia, R. (eds) Algorithms and Data Structures. WADS 1997. Lecture Notes in Computer Science, vol 1272. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63307-3_47
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DOI: https://doi.org/10.1007/3-540-63307-3_47
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