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The Computer Journal Advance Access published online on November 23, 2007
The Computer Journal, doi:10.1093/comjnl/bxm033
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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

The Bidimensionality Theory and Its Algorithmic Applications1

Erik D. Demaine1,* and Mohammad Taghi Hajiaghayi1

1 MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar Street, Cambridge, MA 02139, USA

* Corresponding author: edemaine{at}mit.edu

Received 26 February 2006; revised 10 August 2006

This paper surveys the theory of bidimensionality. This theory characterizes a broad range of graph problems (‘bidimensional’) that admit efficient approximate or fixed-parameter solutions in a broad range of graphs. These graph classes include planar graphs, map graphs, bounded-genus graphs and graphs excluding any fixed minor. In particular, bidimensionality theory builds on the Graph Minor Theory of Robertson and Seymour by extending the mathematical results and building new algorithmic tools. Here, we summarize the known combinatorial and algorithmic results of bidimensionality theory with the high-level ideas involved in their proof; we describe the previous work on which the theory is based and/or extends; and we mention several remaining open problems.

Key Words: graph algorithms • graph minors • bidimensionality

1 A preliminary version of this paper appeared for Proceedings of the 12th International Symposium on Graph Drawing, LNCS 3383, 2004, pages 517–533.


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