Minimum diameter cost-constrained Steiner trees

Wei Ding () and Guoliang Xue ()
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Wei Ding: Zhejiang Water Conservancy and Hydropower College
Guoliang Xue: Arizona State University

Journal of Combinatorial Optimization, 2014, vol. 27, issue 1, No 4, 32-48

Abstract: Abstract Given an edge-weighted undirected graph $$G=(V,E,c,w)$$ where each edge $$e\in E$$ has a cost $$c(e)\ge 0$$ and another weight $$w(e)\ge 0$$ , a set $$S\subseteq V$$ of terminals and a given constant $$\mathrm{C}_0\ge 0$$ , the aim is to find a minimum diameter Steiner tree whose all terminals appear as leaves and the cost of tree is bounded by $$\mathrm{C}_0$$ . The diameter of a tree refers to the maximum weight of the path connecting two different leaves in the tree. This problem is called the minimum diameter cost-constrained Steiner tree problem, which is NP-hard even when the topology of the Steiner tree is fixed. In this paper, we deal with the fixed-topology restricted version. We prove the restricted version to be polynomially solvable when the topology is not part of the input and propose a weakly fully polynomial time approximation scheme (weakly FPTAS) when the topology is part of the input, which can find a $$(1+\epsilon )$$ –approximation of the restricted version problem for any $$\epsilon >0$$ with a specific characteristic.

Keywords: Steiner Tree; Minimum Diameter; Multicast Tree; Steiner Tree Problem; Objective Tree (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10878-013-9611-2

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