Approximation Algorithms via Contraction Decomposition
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Demaine_Approximation algorithms via contraction.pdf
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Author(s)
Hajiaghayi, Mohammad Taghi
Demaine, Erik D.
Mohar, Bojan
Date Issued
September 2010
Journal
Combinatorica
Publisher
Bolyai Society/Springer-Verlag
Citation
Demaine, Erik, MohammadTaghi Hajiaghayi and Bojan Mohar. “Approximation Algorithms via Contraction Decomposition.” Combinatorica 30.5 (2010) : 533-552.
Version
Author's final manuscript
Abstract
We prove that the edges of every graph of bounded (Euler) genus can be partitioned into
any prescribed number k of pieces such that contracting any piece results in a graph of bounded
treewidth (where the bound depends on k). This decomposition result parallels an analogous,
simpler result for edge deletions instead of contractions, obtained in [Bak94, Epp00, DDO+04,
DHK05], and it generalizes a similar result for \compression" (a variant of contraction) in
planar graphs [Kle05]. Our decomposition result is a powerful tool for obtaining PTASs for
contraction-closed problems (whose optimal solution only improves under contraction), a much
more general class than minor-closed problems. We prove that any contraction-closed problem
satisfying just a few simple conditions has a PTAS in bounded-genus graphs. In particular, our
framework yields PTASs for the weighted Traveling Salesman Problem and for minimum-weight
c-edge-connected submultigraph on bounded-genus graphs, improving and generalizing previous
algorithms of [GKP95, AGK+98, Kle05, Gri00, CGSZ04, BCGZ05]. We also highlight the only
main di culty in extending our results to general H-minor-free graphs.
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http://www.springerlink.com/content/h96773m010737357/fulltext.pdf
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
http://dx.doi.org/10.1007/s00493-010-2341-5
https://doi.org/10.1007/s00493-010-2341-5
