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Algorithmic graph minor theory: Decomposition, approximation, and coloring

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3 Author(s)
Demaine, E.D. ; Comput. Sci. & Artificial Intelligence Lab., Massachusetts Inst. of Technol., Cambridge, MA, USA ; Hajiaghayi, M. ; Kawarabayashi, K.

At the core of the seminal graph minor theory of Robertson and Seymour is a powerful structural theorem capturing the structure of graphs excluding a fixed minor. This result is used throughout graph theory and graph algorithms, but is existential. We develop a polynomial-time algorithm using topological graph theory to decompose a graph into the structure guaranteed by the theorem: a clique-sum of pieces almost-embeddable into bounded-genus surfaces. This result has many applications. In particular we show applications to developing many approximation algorithms, including a 2-approximation to graph coloring, constant-factor approximations to treewidth and the largest grid minor, combinatorial polylogarithmic approximation to half-integral multicommodity flow, subexponential fixed-parameter algorithms, and PTASs for many minimization and maximization problems, on graphs excluding a fixed minor.

Published in:

Foundations of Computer Science, 2005. FOCS 2005. 46th Annual IEEE Symposium on

Date of Conference:

23-25 Oct. 2005