10 research outputs found
Polynomial-Time Approximation Schemes for Independent Packing Problems on Fractionally Tree-Independence-Number-Fragile Graphs
We investigate a relaxation of the notion of treewidth-fragility, namely tree-independence-number-fragility. In particular, we obtain polynomial-time approximation schemes for independent packing problems on fractionally tree-independence-number-fragile graph classes. Our approach unifies and extends several known polynomial-time approximation schemes on seemingly unrelated graph classes, such as classes of intersection graphs of fat objects in a fixed dimension or proper minor-closed classes. We also study the related notion of layered tree-independence number, a relaxation of layered treewidth
On dominating set of some subclasses of string graphs
We provide constant factor approximation algorithms for the Minimum Dominating Set
(MDS) problem on several subclasses of string graphs i.e. intersection graphs of simple
curves on the plane. For k ≥ 0, unit Bk-VPG graphs are intersection graphs of simple
rectilinear curves having at most k cusps (bends) and each segment of the curve being
unit length. We give an 18-approximation algorithm for the MDS problem on unit B0-VPG
graphs. This partially addresses a question of Katz et al. (2005) [24]. We also give an O(k4)-
approximation algorithm for the MDS problem on unit Bk-VPG graphs. We show that there
is an 8-approximation algorithm for the MDS problem on vertically-stabbed L-graphs. We
also give a 656-approximation algorithm for the MDS problem on stabbed rectangle overlap
graphs. This is the first constant-factor approximation algorithm for the MDS problem on
stabbed rectangle overlap graphs and extends a result of Bandyapadhyay et al. (2019) [31].
We prove some hardness results to complement the above results
LIPIcs, Volume 258, SoCG 2023, Complete Volume
LIPIcs, Volume 258, SoCG 2023, Complete Volum