Abstract
We prove that for sufficiently large n, there exist unit disk graphs on n vertices such that for every representation with disks in the plane at least \(c^{\sqrt{n}}\) bits are needed to write down the coordinates of the centers of the disks, for some c> 1. We also show that d n bits always suffice, for some d>1.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Breu, H., Kirkpatrick, D.G.: Unit disk graph recognition is NP-hard. Comput. Geom. 9(1-2), 3–24 (1998)
Goodman, J.E., Pollack, R., Sturmfels, B.: The intrinsic spread of a configuration in R d. J. Amer. Math. Soc. 3(3), 639–651 (1990)
Grigor’ev, D.Y., Vorobjov, N.N.: Solving systems of polynomial inequalities in subexponential time. J. Symbolic Comput. 5(1-2), 37–64 (1988)
Kratochvíl, J., Matoušek, J.: Intersection graphs of segments. KAM preprint series. Charles University, Prague (1988)
Kratochvíl, J., Matoušek, J.: Intersection graphs of segments. J. Combin. Theory Ser. B 62(2), 289–315 (1994)
van Leeuwen, E.J., van Leeuwen, J.: On the representation of disk graphs. Utrecht University Technical report number UU-CS-2006-037 (July 2006)
Schrijver, A.: Theory of linear and integer programming. Wiley-Interscience Series in Discrete Mathematics. John Wiley & Sons Ltd., Chichester (1986); A Wiley-Interscience Publication
Spinrad, J.P.: Efficient graph representations. Fields Institute Monographs, vol. 19. American Mathematical Society, Providence (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
McDiarmid, C., Müller, T. (2010). The Number of Bits Needed to Represent a Unit Disk Graph. In: Thilikos, D.M. (eds) Graph Theoretic Concepts in Computer Science. WG 2010. Lecture Notes in Computer Science, vol 6410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16926-7_29
Download citation
DOI: https://doi.org/10.1007/978-3-642-16926-7_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16925-0
Online ISBN: 978-3-642-16926-7
eBook Packages: Computer ScienceComputer Science (R0)