An approximation algorithm for the k-generalized Steiner forest problem

In this paper, we introduce the k -generalized Steiner forest ( k -GSF) problem, which is a natural generalization of the k -Steiner forest problem and the generalized Steiner forest problem. In this problem, we are given a connected graph G = ( V , E ) with non-negative costs c e for the edges e ∈...

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Bibliographic Details
Published in:Optimization letters Vol. 15; no. 4; pp. 1475 - 1483
Main Authors: Gao, Jiawen, Gao, Suogang, Liu, Wen, Wu, Weili, Du, Ding-Zhu, Hou, Bo
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2021
Subjects:
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
Greedy algorithm
generalized Steiner forest problem
LP-rounding algorithm
ISSN:1862-4472, 1862-4480
Online Access:Get full text
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Summary:In this paper, we introduce the k -generalized Steiner forest ( k -GSF) problem, which is a natural generalization of the k -Steiner forest problem and the generalized Steiner forest problem. In this problem, we are given a connected graph G = ( V , E ) with non-negative costs c e for the edges e ∈ E , a set of disjoint vertex sets V = { V 1 , V 2 , … , V l } and a parameter k ≤ l . The goal is to find a minimum-cost edge set F ⊆ E that connects at least k vertex sets in V . Our main work is to construct an O ( l ) -approximation algorithm for the k -GSF problem based on a greedy approach and an LP-rounding technique.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-021-01727-y