科研之友
微信
新浪微博
Facebook
分享链接
摘要
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 [4,20,10,17], and it generalizes a similar result for "compression" (a variant of contraction) in planar graphs [29]. 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 [24,1,29,25,8,5]. We also highlight the only main difficulty in extending our results to general H-minor-free graphs.
- 出版日期2010
