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dc.contributor.authorDemaine, Erik D.
dc.contributor.authorHajiaghayi, Mohammad Taghi
dc.contributor.authorKawarabayashi, Ken-ichi
dc.date.accessioned2011-04-19T20:42:58Z
dc.date.available2011-04-19T20:42:58Z
dc.date.issued2009-07
dc.identifier.isbn9783642029264
dc.identifier.urihttp://hdl.handle.net/1721.1/62243
dc.description.abstractWe develop new structural results for apex-minor-free graphs and show their power by developing two new approximation algorithms. The first is an additive approximation for coloring within 2 of the optimal chromatic number, which is essentially best possible, and generalizes the seminal result by Thomassen [32] for bounded-genus graphs. This result also improves our understanding from an algorithmic point of view of the venerable Hadwiger conjecture about coloring H-minor-free graphs. The second approximation result is a PTAS for unweighted TSP in apex-minor-free graphs, which generalizes PTASs for TSP in planar graphs and bounded-genus graphs [20,2,24,15]. We strengthen the structural results from the seminal Graph Minor Theory of Robertson and Seymour in the case of apex-minor-free graphs, showing that apices can be made adjacent only to vortices if we generalize the notion of vortices to “quasivortices” of bounded treewidth, proving a conjecture from [10]. We show that this structure theorem is a powerful tool for developing algorithms on apex-minor-free graphs, including for the classic problems of coloring and TSP. In particular, we use this theorem to partition the edges of a graph into k pieces, for any k, such that contracting any piece results in a bounded-treewidth graph, generalizing previous similar results for planar graphs [24] and bounded-genus graphs [15]. We also highlight the difficulties in extending our results to general H-minor-free graphs.en_US
dc.language.isoen_US
dc.publisherSpringer Berlin/Heidelbergen_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/978-3-642-02927-1_27en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alike 3.0en_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/en_US
dc.sourceMIT web domainen_US
dc.titleApproximation algorithms via structural results for apex-minor-free graphsen_US
dc.typeArticleen_US
dc.identifier.citationDemaine, Erik, Mohammadtaghi Hajiaghayi, and Ken-ichi Kawarabayashi. “Approximation Algorithms via Structural Results for Apex-Minor-Free Graphs.” Automata, Languages and Programming. Springer Berlin/Heidelberg, 2009. 316-327. (Lecture Notes in Computer Science, 2009, Volume 5555/2009).en_US
dc.contributor.departmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratoryen_US
dc.contributor.approverDemaine, Erik D.
dc.contributor.mitauthorDemaine, Erik D.
dc.relation.journalAutomata, Languages and Programming, 36th International Coloquium, ICALP 2009en_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/ConferencePaperen_US
dspace.orderedauthorsDemaine, Erik D.; Hajiaghayi, MohammadTaghi; Kawarabayashi, Ken-ichien
dc.identifier.orcidhttps://orcid.org/0000-0003-3803-5703
mit.licenseOPEN_ACCESS_POLICYen_US


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