Abstract
Steiner's problem in graphs lies at the very heart of many optimization problems. As the problem is NP-hard, fast and good approximation algorithms are being sought. We discuss some of the most important heuristics. None of these heuristics is superior to any other, neither in terms of speed nor in terms of the quality of the approximate solution. We present and analyze a new algorithm outperforming all of these heuristics in both aspects.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
A.V. Aho, J.E. Hopcroft, J.D. Ullman: The design and analysis of computer algorithms, Addison-Wesley, Reading, Mass., 1974.
E.N. Dijkstra: A note on two problems in connection with graphs, Numer. Math.1, 1959, 269–271.
L.R. Foulds, V.J. Rayward-Smith: Steiner problem in graphs, algorithms and applications, School of Comp. Studies and Accountancy, Univ. East Anglia, Tech. Report, 1983.
M.L. Fredman, R.E. Tarjan: Fibonacci heaps and their uses in improved network optimization algorithms, Ann. Symp. on Foundations of Comp. Science, 1984, 338–346.
E.N. Gilbert, H.O. Pollak: Steiner minimal trees, SIAM J. Appl. Math.16, 1968, 1–29.
R.M. Karp: Reducibility among combinatorial problems, Complexity of computer computations, New York, 1972, 85–103.
L. Kou, G. Markowsky, L. Berman: A fast algorithm for Steiner trees, Acta Informatica15, 1981, 141–145.
J.B. Kruskal Jr.: On the shortest spanning subtree of a graph and the travelling salesman problem, Proc. Amer. Math. Soc. 78, 1956, 48–50.
H. Mori, T. Fujita, H. Wakata, S. Goto: WIREX: VLSI wiring design expert system, Proc. IFIP VLSI 85, Tokyo, 1985, 297–306.
R.C. Prim: Shortest connection networks and some generalizations, Bell System Tech. J.36, 1957, 1398–1401.
H. Takahashi, A. Matsuyama: An approximate solution for the Steiner problem in graphs, Math. Japonica24, 1980, 573–577.
S.M. Wang: A multiple source algorithm for suboptimum Steiner trees in graphs, Proc. Intl. Workshop Graphtheor. Concepts in Comp. Science, ed. H. Noltemeier, Würzburg, 1985, 387–396.
P. Widmayer: Fast approximation algorithms for Steiner's problem in graphs, Institut für Angewandte Informatik und Formale Beschreibungsverfahren, Universität Karlsruhe, 1986.
P. Widmayer, Y.F. Wu, C.K. Wong: On the approximation of Steiner minimal trees in graphs, Institut für Angewandte Informatik und Formale Beschreibungsverfahren, Universität Karlsruhe, Tech. Report, 1985.
Y.F. Wu, P. Widmayer, C.K. Wong: A faster approximation algorithm for the Steiner problem in graphs, IBM Research Report, 1984, to appear in Acta Informatica.
Y.F. Wu, P. Widmayer, M.D.F. Schlag, C.K. Wong: Rectilinear shortest paths and minimum spanning trees in the presence of rectilinear obstacles, Proc. Intl. Workshop Graphtheor. Concepts in Comp. Science, ed. H. Noltemeier, Würzburg, 1985, 405–420.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1987 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Widmayer, P. (1987). On approximation algorithms for Steiner's problem in graphs. In: Tinhofer, G., Schmidt, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 1986. Lecture Notes in Computer Science, vol 246. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-17218-1_46
Download citation
DOI: https://doi.org/10.1007/3-540-17218-1_46
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17218-5
Online ISBN: 978-3-540-47415-9
eBook Packages: Springer Book Archive