We overview the recent progress in solving intractable optimization problems on planar graphs as well as other classes of sparse graphs. In particular, we discuss how tools from Graph Minors theory can be used to obtain: * subexponential parameterized algorithms * approximation algorithms, and * preprocessing and kernelization algorithms on these classes of graphs.
@InProceedings{fomin:LIPIcs.FSTTCS.2016.5, author = {Fomin, Fedor V.}, title = {{Graph Decompositions and Algorithms}}, booktitle = {36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)}, pages = {5:1--5:1}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-027-9}, ISSN = {1868-8969}, year = {2016}, volume = {65}, editor = {Lal, Akash and Akshay, S. and Saurabh, Saket and Sen, Sandeep}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2016.5}, URN = {urn:nbn:de:0030-drops-68903}, doi = {10.4230/LIPIcs.FSTTCS.2016.5}, annote = {Keywords: Algorithms, logic, graph minor} }
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