Approximation Schemes in Planar Graphs

There are growing interests in designing polynomial-time approximation schemes (PTAS) for optimization problems in planar graphs. Many NP-hard problems are shown to admit PTAS in planar graphs in the last decade, including Steiner tree, Steiner forest, two- edge-connected subgraphs and so on. We follow this research line and study several NP- hard problems in planar graphs, including minimum three-vertex-connected spanning subgraph problem, minimum three-edge-connected spanning subgraph problem, relaxed minimum-weight subset three-edge-connected subgraph problem and minimum feedback vertex set problem. For the first three problems, we give the first PTAS results, and for the last problem, we give a PTAS result based on local search and a practical heuristic algorithm that provides a trade-off between running time and solution quality like a PTAS

09511 Abstracts Collection -- Parameterized complexity and approximation algorithms

From 14. 12. 2009 to 17. 12. 2009., the Dagstuhl Seminar 09511 ``Parameterized complexity and approximation algorithms \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Structural Results and Approximation Algorithms in Minor-free Graphs

Planarity has been successfully exploited to design faster and more accurate approximation algorithms for many graph optimization problems. The celebrated theorem of Kuratowski completely characterizes planar graphs as those excluding K_5 and K_{3,3} as minors. Kuratowski's theorem allows one to generalize planar graphs to H-minor-free graphs: those that exclude a fixed graph H as a minor. The deep results of Robertson and Seymour reveal many hidden structures in H-minor-free graphs, that have been used extensively in algorithmic designs. Relying on these structures, we design (i) an (efficient) polynomial time approximation scheme (PTAS) for two different variants of the traveling salesperson problem (TSP) and (ii) simple local search PTASes for r-dominating set and feedback vertex set problems. We then present several results concerning structures of planar graphs. Specifically, we make progresses on two conjectures on existence of large induced forests in planar graphs

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

Visualization Algorithms for Maps and Diagrams

One of the most common visualization tools used by mankind are maps or diagrams. In this thesis we explore new algorithms for visualizing maps (road and argument maps). A map without any textual information or pictograms is often without use so we research also further into the field of labeling maps. In particular we consider the new challenges posed by interactive maps offered by mobile devices. We discuss new algorithmic approaches and experimentally evaluate them

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum