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Latin American Symposium on Theoretical Informatics

LATIN 2008: LATIN 2008: Theoretical Informatics pp 654–663Cite as

Paths with no Small Angles

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4957))

Abstract

Giving a partial solution to a problem of S. Fekete and G.J. Woeginger [3,4] we show that given a finite set X of points in the plane, it is possible to arrange them on a polygonal path (with the vertex set X) so that every angle on the polygonal path is at least π/9. According to a conjecture of Fekete and Woeginger, π/9 can be replaced by π/6. Previously, the result has not been known with any positive constant.

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References

  1. Aichholzer, O., Hackl, T., Hoffmann, M., Huemer, C., Pór, A., Santos, F., Speckmann, B., Vogtenhuber, B.: Maximizing Maximal Angles for Plane Straight-Line Graphs. In: Dehne, F., Sack, J.-R., Zeh, N. (eds.) WADS 2007. LNCS, vol. 4619, pp. 458–469. Springer, Heidelberg (2007)

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  2. Bárány, I., Pór, A., Valtr, P.: Paths with no small angles (manuscript in preparation, 2007)

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  3. Fekete, S.: Geometry and the Travelling Salesman Problem, Ph.D. thesis, University of Waterloo (1992)

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  4. Fekete, S., Woeginger, G.J.: Angle-restricted tours in the plane. Comput. Geom.: Theory and Appl. 8, 195–218 (1997)

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  5. Kirkpatrick, Seidel, R.: The ultimate planar convex hull algorithm. SIAM J. Computing 15, 286–297 (1986)

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Author information

Authors and Affiliations

  1. Rényi Institute of Mathematics, Hungarian Academy of Sciences, POBox 127, 1364, Budapest, Hungary

    Imre Bárány

  2. Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, England

    Imre Bárány

  3. Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00, Praha 1, Czech Republic

    Attila Pór & Pavel Valtr

Authors
  1. Imre Bárány
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  2. Attila Pór
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  3. Pavel Valtr
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Editor information

Eduardo Sany Laber Claudson Bornstein Loana Tito Nogueira Luerbio Faria

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© 2008 Springer-Verlag Berlin Heidelberg

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Bárány, I., Pór, A., Valtr, P. (2008). Paths with no Small Angles. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds) LATIN 2008: Theoretical Informatics. LATIN 2008. Lecture Notes in Computer Science, vol 4957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78773-0_56

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  • DOI: https://doi.org/10.1007/978-3-540-78773-0_56

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78772-3

  • Online ISBN: 978-3-540-78773-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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