Node-Weighted Steiner Tree and Group Steiner Tree in Planar Graphs
Name
NodePlanarSteiner.pdf
Description
Accepted version
Size
237.54 KB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Demaine, Erik D
Hajiaghayi, Mohammadtaghi
Klein, Philip N
Date Issued
2014
Journal
ACM Transactions on Algorithms
Publisher
Association for Computing Machinery (ACM)
Version
Author's final manuscript
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(log n), 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, prizecollecting 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 n), or O(log2 n) when the host graph is a tree. We obtain an O(log npolyloglog 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. © 2014 ACM.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1145/2601070
