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dc.contributor.authorDemaine, Erik D.
dc.contributor.authorHajiaghayi, Mohammad Taghi
dc.contributor.authorKlein, Philip N.
dc.date.accessioned2011-04-20T19:36:55Z
dc.date.available2011-04-20T19:36:55Z
dc.date.issued2009
dc.identifier.issn0170-1495
dc.identifier.urihttp://hdl.handle.net/1721.1/62256
dc.description.abstractWe improve the approximation ratios for two optimization problems in planar graphs. For node-weighted Steiner tree, a classical network-optimization problem, the best achievable approximation ratio in general graphs is Θ [theta] (logn), and nothing better was previously known for planar graphs. We give a constant-factor approximation for planar graphs. Our algorithm generalizes to allow as input any nontrivial minor-closed graph family, and also generalizes to address other optimization problems such as Steiner forest, prize-collecting Steiner tree, and network-formation games. The second problem we address is group Steiner tree: given a graph with edge weights and a collection of groups (subsets of nodes), find a minimum-weight connected subgraph that includes at least one node from each group. The best approximation ratio known in general graphs is O(log3 [superscript 3] n), or O(log2 [superscript 2] n) when the host graph is a tree. We obtain an O(log n polyloglog n) approximation algorithm for the special case where the graph is planar embedded and each group is the set of nodes on a face. We obtain the same approximation ratio for the minimum-weight tour that must visit each group.en_US
dc.language.isoen_US
dc.publisherSpringeren_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/978-3-642-02927-1_28en_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.titleNode-weighted Steiner tree and group Steiner tree in planar graphsen_US
dc.typeArticleen_US
dc.identifier.citationDemaine, Erik, Mohammadtaghi Hajiaghayi, and Philip Klein. “Node-Weighted Steiner Tree and Group Steiner Tree in Planar Graphs.” Automata, Languages and Programming. (Lecture notes in computer science, v. 5555) Springer Berlin / Heidelberg, 2009. 328-340. Copyright © 2009, Springeren_US
dc.contributor.departmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratoryen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Scienceen_US
dc.contributor.approverDemaine, Erik D.
dc.contributor.mitauthorDemaine, Erik D.
dc.relation.journalAutomata, languages, and programming.en_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/ConferencePaperen_US
dspace.orderedauthorsDemaine, Erik D.; Hajiaghayi, MohammadTaghi; Klein, Philip N.en
dc.identifier.orcidhttps://orcid.org/0000-0003-3803-5703
mit.licenseOPEN_ACCESS_POLICYen_US
mit.metadata.statusComplete


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