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The Computer Journal Advance Access originally published online on July 27, 2007
The Computer Journal 2008 51(3):372-384; doi:10.1093/comjnl/bxm053
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© The Author 2007. Published by Oxford University Press on behalf of The British Computer Society. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Parameterized Complexity of Geometric Problems

Panos Giannopoulos1,*, Christian Knauer2 and Sue Whitesides3

1 Institut für Informatik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
2 Institut für Informatik, Freie Universität Berlin, Takustraße 9, D–14195 Berlin, Germany
3 School of Computer Science, McGill University, 3480 University Street, Montreal, Canada H3A 2A7

* Corresponding author: panos{at}informatik.hu-berlin.de

Received 5 February 2007; revised 31 March 2007

This paper surveys parameterized complexity results for hard geometric algorithmic problems. It includes fixed-parameter tractable problems in graph drawing, geometric graphs, geometric covering and several other areas, together with an overview of the algorithmic techniques used. Fixed-parameter intractability results are surveyed as well. Finally, we give some directions for future research.

Key Words: Computational geometry • graph drawing • Parameterized algorithms


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