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Eun Jung Kim (김은정), A Constant-factor Approximation for Weighted Bond Cover

August 24 Tuesday @ 4:30 PM - 5:30 PM KST

Room B232, IBS (기초과학연구원)

The Weighted $\mathcal F$-Vertex Deletion for a class $\mathcal F$ of graphs asks, given a weighted graph $G$, for a minimum weight vertex set $S$ such that $G-S\in\mathcal F$. The case when $\mathcal F$ is minor-closed and excludes some graph as a minor has received particular attention but a constant-factor approximation remained elusive for Weighted $\mathcal F$-Vertex Deletion. Only three cases of minor-closed $\mathcal F$ are known to admit constant-factor approximations, namely Vertex Cover, Feedback Vertex Set and Diamond Hitting Set.

We study the problem for the class $\mathcal F$ of $\theta_c$-minor-free graphs, under the equivalent setting of the Weighted c-Bond Cover, and present a constant-factor approximation algorithm using the primal-dual method. For this, we leverage a structure theorem implicit in [Joret et al., SIDMA’14] which states the following: any graph $G$ containing a $\theta_c$-minor-model either contains a large two-terminal protrusion, or contains a constant-size $\theta_c$-minor-model, or a collection of pairwise disjoint constant-sized connected sets that can be contracted simultaneously to yield a dense graph. In the first case, we tame the graph by replacing the protrusion with a special-purpose weighted gadget. For the second and third case, we provide a weighting scheme which guarantees a local approximation ratio. Besides making an important step in the quest of (dis)proving a constant-factor approximation for Weighted $\mathcal F$-Vertex Deletion, our result may be useful as a template for algorithms for other minor-closed families.

This is joint work with Euiwoong Lee and Dimitrios M. Thilikos.

Details

Date:
August 24 Tuesday
Time:
4:30 PM - 5:30 PM KST
Event Category:
Event Tags:
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Venue

Room B232
IBS (기초과학연구원)

Organizer

Sang-il Oum (엄상일)
View Organizer Website
IBS 이산수학그룹 Discrete Mathematics Group
기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr, Fax: +82-42-878-9209
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