Finding thek smallest spanning trees
- David Eppstein
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We give improved solutions for the problem of generating thek smallest spanning trees in a graph and in the plane. Our algorithm for general graphs takes timeO(m logβ(m, n)=k 2); for planar graphs this bound can be improved toO(n+k 2). We also show that thek best spanning trees for a set of points in the plane can be computed in timeO(min(k 2 n+n logn,k 2+kn log(n/k))). Thek best orthogonal spanning trees in the plane can be found in timeO(n logn+kn log log(n/k)+k 2).
- A. Aggarwal, L. J. Guibas, J. Saxe, and P. W. Shor,A linear time algorithm for computing the Voronoi diagram of a convex polygon, Discrete and Comput. Geom. 4, 1989, 591–604.
- A. Aggarwal, H. Imai, N. Katoh, and S. Suri,Finding k points with minimum diameter and related problems, J. Algorithms, to appear.
- A. Aggarwal and J. Wein,Computational Geometry, MIT LCS Research Seminar Series 3, 1988.
- M. Blum, R. W. Floyd, V. R. Pratt, R. L. Rivest, and R. E. Tarjan,Time bounds for selection, J. Comput. Syst. Sci. 7, 1972, 448–461.
- H. Booth and J. Westbrook,Linear algorithms for analysis of minimum spanning and shortest path trees in planar graphs, Tech. Rep. TR-763, Department of Computer Science, Yale University, Feb. 1990.
- R. N. Burns and C. E. Haff,A ranking problem in graphs, 5th Southeast Conf. Combinatorics, Graph Theory and Computing 19, 1974, 461–470.
- P. M. Camerini, L. Fratta, and F. Maffioli,The k shortest spanning trees of a graph, Int. Rep. 73-10, IEEE-LCE Politechnico di Milano, Italy, 1974.
- D. Cheriton and R. E. Tarjan,Finding minimum spanning trees, SIAM J. Comput. 5, 1976, 310–313.
- L. P. Chew and S. Fortune,Sorting helps for Voronoi diagrams, 13th Symp. Mathematical Progr., Japan, 1988.
- D. Eppstein,Offline algorithms for dynamic minimum spanning tree problems, 2nd Worksh. Algorithms and Data Structures, Springer Verlag LNCS 519, 1991, 392–399.
- D. Eppstein, Z. Galil, R. Giancarlo, and G. F. Italiano,Sparse dynamic programming, 1st ACM-SIAM Symp. Discrete Algorithms, San Francisco, 1990. 513–522.
- D. Eppstein, G. F. Italiano, R. Tamassia, R. E. Tarjan, J. Westbrook, and M. Yung,Maintenance of a minimum spanning forest in a dynamic planar graph, 1st ACM-SIAM Symp. Discrete Algorithms, 1990, 1–11.
- G. N. Frederickson,Data structures for on-line updating of minimum spanning trees, SIAM J. Comput. 14(4), 1985, 781–798.
- G. N. Frederickson,Ambivalent data structures for dynamic 2-edge-connectivity and k smallest spanning trees, 32nd IEEE Conf. Foundations of Computer Science, 1991, to appear.
- H. N. Gabow,Two algorithms for generating weighted spanning trees in order, SIAM J. Comput. 6, 1977, 139–150.
- H. N. Gabow, Z. Galil, T. H. Spencer, and R. E. Tarjan,Efficient algorithms for minimum spanning trees on directed and undirected graphs, Combinatorica 6, 1986, 109–122.
- H. N. Gabow and M. Stallman,Efficient algorithms for graphic matroid intersection and parity, 12th Int. Conf. Automata, Languages, and Programming, Springer-Verlag LNCS 194, 1985, 210–220.
- N. Katoh, T. Ibaraki, and H. Mine,An algorithm for finding k minimum spanning trees, SIAM J. Comput. 10, 1981, 247–255.
- E. W. Mayr and C. G. Plaxton,On the spanning trees of weighted graphs, manuscript, 1990.
- N. Sarnak and R. E. Tarjan,Planar point location using persistent search trees, C. ACM 29(7), 1986, 669–679.
- R. E. Tarjan,Applications of path compression on balanced trees, J. ACM 26, 1979, 690–715.
- P. van Emde Boas,Preserving order in a forest in less than logarithmic time, 16th IEEE Symp. Found. Comput. Sci., 1975, and Info. Proc. Lett. 6, 1977, 80–82.
- Finding thek smallest spanning trees
BIT Numerical Mathematics
Volume 32, Issue 2 , pp 237-248
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- 1. Department of Information and Computer Science, University of California, 92717, Irvine, CA, USA