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Area requirement of Gabriel drawings (extended abstract)

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Algorithms and Complexity (CIAC 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1203))

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Abstract

In this paper we investigate the area requirement of proximity drawings and we prove an exponential lower bound. Our main contribution is to show the existence of a class of Gabriel-drawable graphs that require exponential area for any Gabriel drawing and any resolution rule. The result is further extended to an infinite class of proximity drawings.

Work supported in part by the US National Science Foundation under grant CCR-9423847, by the US Army Research Office under grant DAAH04-96-1-0013, by the NATO Scientific Affairs Division under collaborative research grant 911016, by EC ESPRIT Long Term Research Project ALCOM-IT under contract no. 20244, by Progetto Finalizzato Trasporti 2 (PFT 2) of the Italian National Research Council (CNR), and by the NATO-CNR Advanced Fellowships Programme. This research was done when the first author was with the Center for Geometric Computing, Department of Computer Science, Brown University,Providence, RI 02912-1910, USA. This research started while the fourth author was visiting the Computer Science Department of Brown University.

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica e Sistemistica, Universitá di Roma “La Sapienza”, via Salaria 113, 00198, Rome, Italy

    G. Liotta

  2. Center for Geometric Computing, Department of Computer Science, Brown University, 02912-1910, Providence, RI, USA

    R. Tamassia

  3. Department of Computer Science, The University of Texas at Dallas, 75083-0688, Richardson, TX, USA

    I. G. Tollis

  4. Dipartimento di Matematica, University of Rome “Tor Vergata”, via della Ricerca, Scientifica, 00133, Rome, Italy

    P. Vocca

Authors
  1. G. Liotta
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  2. R. Tamassia
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  3. I. G. Tollis
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  4. P. Vocca
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Editor information

Giancarlo Bongiovanni Daniel Pierre Bovet Giuseppe Di Battista

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© 1997 Springer-Verlag Berlin Heidelberg

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Liotta, G., Tamassia, R., Tollis, I.G., Vocca, P. (1997). Area requirement of Gabriel drawings (extended abstract). In: Bongiovanni, G., Bovet, D.P., Di Battista, G. (eds) Algorithms and Complexity. CIAC 1997. Lecture Notes in Computer Science, vol 1203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62592-5_67

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  • DOI: https://doi.org/10.1007/3-540-62592-5_67

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