Paper by Erik D. Demaine

Reference:

Erik D. Demaine, MohammadTaghi Hajiaghayi, and Dimitrios M. Thilikos, “The Bidimensional Theory of Bounded-Genus Graphs”, in Proceedings of the 29th International Symposium on Mathematical Foundations of Computer Science (MFCS 2004), Prague, Czech Republic, August 22–27, 2004, pages 191–203.

Abstract:

Bidimensionality is a powerful tool for developing subexponential fixed-parameter algorithms for combinatorial optimization problems on graph families that exclude a minor. This paper completes the theory of bidimensionality for graphs of bounded genus (which is a minor-excluding family). Specifically we show that, for any problem whose solution value does not increase under contractions and whose solution value is large on a grid graph augmented by a bounded number of handles, the treewidth of any bounded-genus graph is at most a constant factor larger than the square root of the problem's solution value on that graph. Such bidimensional problems include vertex cover, feedback vertex set, minimum maximal matching, dominating set, edge dominating set, r-dominating set, connected dominating set, planar set cover, and diameter. This result has many algorithmic and combinatorial consequences. On the algorithmic side, by showing that an augmented grid is the prototype bounded-genus graph, we generalize and simplify many existing algorithms for such problems in graph classes excluding a minor. On the combinatorial side, our result is a step toward a theory of graph contractions analogous to the seminal theory of graph minors by Robertson and Seymour.

Length:

The paper is 12 pages.

Availability:

The paper is available in PostScript (483k), gzipped PostScript (193k), and PDF (204k).

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