Approximation algorithms via contraction decomposition (2007)
| Venue: | Proc. 18th Ann. ACM-SIAM Symp. Discrete Algorithms ACM-SIAM symposium on Discrete algorithms |
| Citations: | 20 - 6 self |
BibTeX
@INPROCEEDINGS{Demaine07approximationalgorithms,
author = {Erik D. Demaine and Mohammadtaghi Hajiaghayi and Bojan Mohar},
title = {Approximation algorithms via contraction decomposition},
booktitle = {Proc. 18th Ann. ACM-SIAM Symp. Discrete Algorithms ACM-SIAM symposium on Discrete algorithms},
year = {2007},
pages = {278--287}
}
Bookmark
 |
 |
 |
 |
 |
 |
OpenURL
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 difficulty in extending our results to general H-minor-free graphs.
