dc.contributor.author | Demaine, Erik D. | |
dc.contributor.author | Hajiaghayi, Mohammad Taghi | |
dc.contributor.author | Klein, Philip N. | |
dc.date.accessioned | 2011-04-20T19:36:55Z | |
dc.date.available | 2011-04-20T19:36:55Z | |
dc.date.issued | 2009 | |
dc.identifier.issn | 0170-1495 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/62256 | |
dc.description.abstract | We 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.iso | en_US | |
dc.publisher | Springer | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1007/978-3-642-02927-1_28 | en_US |
dc.rights | Creative Commons Attribution-Noncommercial-Share Alike 3.0 | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/3.0/ | en_US |
dc.source | MIT web domain | en_US |
dc.title | Node-weighted Steiner tree and group Steiner tree in planar graphs | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Demaine, 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, Springer | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science | en_US |
dc.contributor.approver | Demaine, Erik D. | |
dc.contributor.mitauthor | Demaine, Erik D. | |
dc.relation.journal | Automata, languages, and programming. | en_US |
dc.eprint.version | Author's final manuscript | en_US |
dc.type.uri | http://purl.org/eprint/type/ConferencePaper | en_US |
dspace.orderedauthors | Demaine, Erik D.; Hajiaghayi, MohammadTaghi; Klein, Philip N. | en |
dc.identifier.orcid | https://orcid.org/0000-0003-3803-5703 | |
mit.license | OPEN_ACCESS_POLICY | en_US |
mit.metadata.status | Complete | |