Node-Weighted Steiner Tree and Group Steiner Tree in Planar Graphs
نویسندگان
چکیده
منابع مشابه
Node-weighted Steiner tree approximation in unit disk graphs
Given a graph G = (V ,E) with node weight w : V → R+ and a subset S ⊆ V , find a minimum total weight tree interconnecting all nodes in S. This is the node-weighted Steiner tree problem which will be studied in this paper. In general, this problem is NP-hard and cannot be approximated by a polynomial time algorithm with performance ratio a lnn for any 0 < a < 1 unless NP ⊆ DTIME(nO(logn)), wher...
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Given a node-weighted connected graph and a subset of terminals, the problem node-weighted Steiner tree (NWST) seeks a lightest tree connecting a given set of terminals in a node-weighted graph. While NWST in general graphs are as hard as Set Cover, NWST restricted to unit-disk graphs (UDGs) admits X. Xu, H. Du, P.-J. Wan were supported in part by NSF under grant CNS-0831831. Y. Wang was suppor...
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Abstract. We study the prize-collecting version of the Node-weighted Steiner Tree problem (NWPCST) restricted to planar graphs. We give a new primal-dual Lagrangian-multiplier-preserving (LMP) 3-approximation algorithm for planar NWPCST. We then show a (2.88+ǫ)-approximation which establishes a new best approximation guarantee for planar NWPCST. This is done by combining our LMP algorithm with ...
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We obtain polynomial-time approximation-preserving reductions (up to a factor of 1+ε) from the prizecollecting Steiner tree and prize-collecting Steiner forest problems in planar graphs to the corresponding problems in graphs of bounded treewidth. We also give an exact algorithm for the prize-collecting Steiner tree problem that runs in polynomial time for graphs of bounded treewidth. This, com...
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We consider a class of optimization problems, where the input is an undirected graph with two weight functions dened for each node, namely the node's pro t and its cost. The goal is to nd a connected set of nodes of low cost and high pro t. We present approximation algorithms for three natural optimization criteria that arise in this context, all of which are NP-hard. The budget problem asks fo...
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ژورنال
عنوان ژورنال: ACM Transactions on Algorithms
سال: 2014
ISSN: 1549-6325,1549-6333
DOI: 10.1145/2601070