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COMBINATORICA
2010

Approximation algorithms via contraction decomposition

11 years 8 months ago
Approximation algorithms via contraction decomposition
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 boundedgenus graphs. In particular, our framework yields PTASs for the weighted Traveling Salesman Problem and for minimumweight c-edge-connected submultigraph on bounded-genus graphs, improving a...
Erik D. Demaine, MohammadTaghi Hajiaghayi, Bojan M
Added 14 May 2011
Updated 14 May 2011
Type Journal
Year 2010
Where COMBINATORICA
Authors Erik D. Demaine, MohammadTaghi Hajiaghayi, Bojan Mohar
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