Algorithms for finding non-crossing paths with minimum total length in plane graphs
Let G be an undirected plane graph with non-negative edge length, and let k terminal pairs lie on two specified face boundaries. This paper presents an algorithm for finding k “non-crossing paths” in G, each connecting a terminal pair, whose total length is minimum. Here “non-crossing paths” may share common vertices or edges but do not cross each other in the plane. The algorithm runs in time O(n log n) where n is the number of vertices in G.
KeywordsShort Path Grid Graph Face Boundary Middle Generation Terminal Pair
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- [AHU]A.V. Aho, J. E. Hopcroft and J. D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, MA (1974).Google Scholar
- [GT]H. N. Gabow and R. E. Tarjan, A linear-time algorithm for a special case of disjoint set union, Journal of Computer and System Sciences, 30, pp. 209–221 (1985).Google Scholar
- [KL]M. R. Kramer and J. van Leewen, Wire-routing is NP-complete, Report No. RUU-CS-82-4, Department of Computer Science, University of Utrecht, Utrecht, the Netherlands (1982).Google Scholar
- [Lyn]J. F. Lynch, The equivalence of theorem proving and the interconnection problem, ACM SIGDA, The Netherlands (1982).Google Scholar
- [SAN]H. Suzuki, T. Akama and T. Nishizeki, Finding Steiner forests in planar graphs, Proc. of First Siam-ACM Soda, pp. 444–453 (1990).Google Scholar
- [Tar]R.E. Tarjan, Data Structures and Network Algorithms, SIAM, Philadelphia, PA (1983).Google Scholar