Exact Steiner Trees in Graphs and Grid Graphs
Given a graph with nonnegative edge lengths and a selected subset of vertices, the Steiner tree problem is to find a tree of minimum length that spans the selected vertices. This problem is also commonly called the graphical Steiner minimal tree problem or GSMT problem for short. We call the selected vertices terminals. In a Steiner tree, any vertex which is not a terminal and has degree at least three is called a Steiner vertex.
KeywordsPlanar Graph Steiner Tree Boundary Vertex Steiner Tree Problem Grid Graph
Unable to display preview. Download preview PDF.
- M. Bern, Network design problems: Steiner trees and spanning k-trees, Ph.D. thesis, Computer Science Division, University of California at Berkeley, 1987.Google Scholar
- M. Bern and R.L. Graham, The shortest-network problem, Scientific American, January (1989) pp. 84–89.Google Scholar
- M. Brazil, D.A. Thomas, and J.F. Weng, Rectilinear Steiner minimal trees on parallel lines, in D.Z. Du, J.M. Smith, and J.H. Rubinstein (eds.) Advances in Steiner trees, (Kluwer Academic Publishers, 1998).Google Scholar
- M. Brazil, D.A. Thomas, and J.F. Weng, A polynomial time algorithm for rectilinear Steiner trees with terminals constrained to curves, manuscript, 1998.Google Scholar
- S.W. Cheng, Steiner tree for terminals on the boundary of a rectilinear polygon, Proceedings of DIMACS workshop on network connectivity and facilities location, April 28–30, 1997, (DIMACS Series in Discrete Mathematics and Theoretical Computer Science 40, 1998) pp. 39–57.Google Scholar
- S.W. Cheng, A. Lim, and C.T. Wu, Optimal Steiner trees for extremal point sets, Proceedings of International Symposium on Algorithms and Computation, 1993 pp. 523–532.Google Scholar
- S.W. Cheng and C.K. Tang, Fast algorithms for optimal Steiner trees for extremal point sets, Proceedings of International Symposium on Algorithms and Computation, 1995 pp. 322–331.Google Scholar
- T.H. Cormen, C.E. Leiserson, and R.L. Rivest, Introduction to Algorithms, (Cambridge, Massachusetts, The MIT Press, 1994).Google Scholar
- M.L. Fredman and R.E. Tarjan, Fibonacci heaps and their uses in improved network optimization algorithms, Journal of ACM, Vol.16 (1987) pp. 1004–1023.Google Scholar
- S.L. Hakimi, Steiner’s problem in graphs and its implications, Networks, Vol.l (1971) pp. 113–133.Google Scholar
- C.E. Leiserson and F.M. Maley, Algorithms for routing and testing routability of planar VLSI layouts, Proceedings of the 17th Annual ACM Symposium on the Theory of Computing, 1985 pp. 69–78.Google Scholar
- F.M. Maley, Single-Layer Wire Routing and Compaction, (Cambridge, Massachusetts, The MIT Press, 1990).Google Scholar