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On the crossing-free, rectangular embedding of weighted graphs in the plane

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Theoretical Computer Science

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 145))

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Abstract

In [1] M.J.Fischer and M.S.Paterson pointed out that finding the optimal planar layout of a weighted graph with respect to the L2-metric is NP-hard. We consider this problem with respect to the L1-city-block metric in the discrete and continuous case and show that it remains NP-hard.

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References

  1. M.J.Fischer, M.S.Paterson: Optimal Tree Layout (Preliminary Version); Proc. Twelfth Annual ACM Symposium on Theory of Computing, pp. 177–189, 1980

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  2. B. Becker: Über die kreuzungsfreie, rechtwinklige Einbettung von gewichteten Graphen in die Ebene; Dissertation, Saarbrücken 1982

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  3. M.Tompa: An Optimal Solution to a Wire-routing Problem; Proc. Twelfth Annual ACM Symposium on Theory of Computing, pp. 201–210, 1980

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  4. A.S.LaPaugh: A Polynomial Time Algorithm for Optimal Routing around a Rectangle; Proc. Twenty-first Annual IEEE Symposium on Foundations of Computer Science, pp. 282–293, 1980

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  5. D.Dolev, K.Karplus, A.Siegel, A.Strong, J.D.Ullman: Optimal Wiring between Rectangles; Proc. Thirteenth Annual ACM Symposium on Theory of Computing, pp. 312–317, 1981

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Armin B. Cremers Hans-Peter Kriegel

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© 1982 Springer-Verlag Berlin Heidelberg

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Becker, B. (1982). On the crossing-free, rectangular embedding of weighted graphs in the plane. In: Cremers, A.B., Kriegel, HP. (eds) Theoretical Computer Science. Lecture Notes in Computer Science, vol 145. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036469

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  • DOI: https://doi.org/10.1007/BFb0036469

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11973-9

  • Online ISBN: 978-3-540-39421-1

  • eBook Packages: Springer Book Archive

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