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Multi-parameter Minimum Spanning Trees

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1776))

Abstract

A framework for solving certain multidimensional parametric search problems in randomized linear time is presented, along with its application to optimization on matroids, including parametric minimum spanning trees on planar and dense graphs.

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References

  1. Agarwal, P.K., Eppstein, D., Guibas, L.J., Henzinger, M.R.: Parametric and kinetic minimum spanning trees. In: Proceedings 39th IEEE Symp. on Foundations of Computer Science (1998)

    Google Scholar 

  2. Agarwal, P.K., Sharir, M.: Algorithmic techniques for geometric optimization. In: van Leeuwen, J. (ed.) Computer Science Today: Recent Trends and Developments. LNCS, vol. 1000. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  3. Agarwal, P.K., Sharir, M., Toledo, S.: An efficient multidimensional searching technique and its applications. Technical Report CS-1993-20, Computer Science Department, Duke University (July 1993)

    Google Scholar 

  4. Agarwala, R., Fernández-Baca, D.: Weighted multidimensional search and its application to convex optimization. SIAM J. Computing 25, 83–99 (1996)

    Article  MathSciNet  Google Scholar 

  5. Camerini, P.M., Maffioli, F., Vercellis, C.: Multi-constrained matroidal knapsack problems. Mathematical Programming 45, 211–231 (1989)

    Article  MathSciNet  Google Scholar 

  6. Chazelle, B.: Cutting hyperplanes for divide-and-conquer. Discrete Comput. Geom. 9(2), 145–158 (1993)

    Article  MathSciNet  Google Scholar 

  7. Chazelle, B.: A faster deterministic algorithm for minimum spanning trees. In: Proceedings 38th IEEE Symp. on Foundations of Computer Science, pp. 22–31 (1997)

    Google Scholar 

  8. Chazelle, B., Friedman, J.: A deterministic view of random sampling and its use in geometry. Combinatorica 10(3), 229–249 (1990)

    Article  MathSciNet  Google Scholar 

  9. Clarkson, K.L.: Linear programming in \(O (n{\times}3^{{d}^{2}})\) time. Information Processing Letters 22, 21–24 (1986)

    Article  MathSciNet  Google Scholar 

  10. Cohen, E., Megiddo, N.: Maximizing concave functions in fixed dimension. In: Pardalos, P.M. (ed.) Complexity in Numerical Optimization, pp. 74–87. World Scientific, Singapore (1993)

    Chapter  Google Scholar 

  11. Cole, R., Salowe, J.S., Steiger, W.L., Szemerédi, E.: An optimal-time algorithm for slope selection. SIAM J. Computing 18, 792–810 (1989)

    Article  MathSciNet  Google Scholar 

  12. Dyer, M.E.: On a multidimensional search technique and its application to the euclidean one-centre problem. SIAM J. Computing 15(3), 725–738 (1986)

    Article  MathSciNet  Google Scholar 

  13. Edelsbrunner, H.: Algorithms in Combinatorial Geometry. Springer, Heidelberg (1987)

    Book  Google Scholar 

  14. Eppstein, D.: Geometric lower bounds for parametric matroid optimization. Dis-crete Comput. Geom. 20, 463–476 (1998)

    Article  MathSciNet  Google Scholar 

  15. Eppstein, D., Galil, Z., Italiano, G.F., Nissenzweig, A.: Sparsification — a technique for speeding up dynamic graph algorithms. J. Assoc. Comput. Mach. 44, 669–696 (1997)

    Article  MathSciNet  Google Scholar 

  16. Eppstein, D., Galil, Z., Italiano, G.F., Spencer, T.H.: Separator-based sparsification I: planarity testing and minimum spanning trees. J. Computing and Systems Sciences 52, 3–27 (1996)

    Article  MathSciNet  Google Scholar 

  17. Fernández-Baca, D., Slutzki, G.: Linear-time algorithms for parametric min- imum spanning tree problems on planar graphs. Theoretical Computer Science 181, 57–74 (1997)

    Article  MathSciNet  Google Scholar 

  18. Fernández-Baca, D., Slutzki, G.: Optimal parametric search on graphs of bounded tree-width. Journal of Algorithms 22, 212–240 (1997)

    Article  MathSciNet  Google Scholar 

  19. Fernández-Baca, D., Slutzki, G., Eppstein, D.: Using sparsification for parametric minimum spanning tree problems. Nordic Journal of Computing 34(4), 352–366 (1996)

    MathSciNet  MATH  Google Scholar 

  20. Frederickson, G.N.: Optimal algorithms for partitioning trees and locating p-centers in trees. Technical Report CSD-TR 1029, Department of Computer Science, Purdue University, Lafayette, IN (October 1990)

    Google Scholar 

  21. Karger, D.R., Klein, P.N., Tarjan, R.E.: A randomized linear-time algorithm for finding minimum spanning trees. J. Assoc. Comput. Mach. 42, 321–328 (1995)

    Article  MathSciNet  Google Scholar 

  22. Klein, P.N., Rao, S., Rauch, M., Subramanian, S.: Faster shortest-path algorithms for planar graphs. In: Proceedings of the 26th Annual ACM Symposium on Theory of Computing, pp. 27–37 (1994)

    Google Scholar 

  23. Megiddo, N.: Combinatorial optimization with rational objective functions. Math. Oper. Res. 4, 414–424 (1979)

    Article  MathSciNet  Google Scholar 

  24. Megiddo, N.: Applying parallel computation algorithms in the design of serial algorithms. J. Assoc. Comput. Mach. 30(4), 852–865 (1983)

    Article  MathSciNet  Google Scholar 

  25. Megiddo, N.: Linear programming in linear time when the dimension is fixed. J. Assoc. Comput. Mach. 34(1), 200–208 (1984)

    MathSciNet  MATH  Google Scholar 

  26. Norton, C.H., Plotkin, S.A., Tardos, É.: Using separation algorithms in fixed dimension. Journal of Algorithms 13, 79–98 (1992)

    Article  MathSciNet  Google Scholar 

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© 2000 Springer-Verlag Berlin Heidelberg

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Fernández-Baca, D. (2000). Multi-parameter Minimum Spanning Trees. In: Gonnet, G.H., Viola, A. (eds) LATIN 2000: Theoretical Informatics. LATIN 2000. Lecture Notes in Computer Science, vol 1776. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10719839_22

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  • DOI: https://doi.org/10.1007/10719839_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67306-4

  • Online ISBN: 978-3-540-46415-0

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