Parallel Greedy Algorithms for Steiner Forest

The Steiner Forest Problem is a fundamental combinatorial optimization problem in operations research and computer science. Given an undirected graph with non-negative weights for edges and a set of pairs of vertices called terminals, the Steiner Forest Problem is to find the minimum cost subgraph t...

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Bibliographic Details
Published in:IEEE transactions on parallel and distributed systems Vol. 36; no. 6; pp. 1311 - 1325
Main Authors: Ghalami, Laleh, Grosu, Daniel
Format: Journal Article
Language:English
Published: IEEE 01.06.2025
Subjects:
Approximation algorithms
Costs
Forestry
Greedy algorithms
Libraries
multi-core
Optimization
Parallel algorithms
Partitioning algorithms
Steiner forest
Steiner trees
Training
ISSN:1045-9219, 1558-2183
Online Access:Get full text
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Summary:The Steiner Forest Problem is a fundamental combinatorial optimization problem in operations research and computer science. Given an undirected graph with non-negative weights for edges and a set of pairs of vertices called terminals, the Steiner Forest Problem is to find the minimum cost subgraph that connects each of the terminal pairs together. We design a family of parallel greedy algorithms based on a sequential heuristic greedy algorithm called Paired Greedy, which iteratively connects the terminal pairs that have the minimum distance. The family of parallel algorithms consists of a set of algorithms exhibiting various degrees of parallelism determined by the number of pairs that are connected in parallel in each iteration of the algorithms. We implement and run the algorithms on a multi-core system and perform an extensive experimental analysis. We analyzed the performance of the algorithms on a rich library of Steiner Forest instances with various underlying graph types. The results show that our proposed parallel algorithms achieve significant speedup with respect to the sequential Paired Greedy algorithm and provide solutions with costs that are very close to those of the solutions obtained by the sequential Paired Greedy algorithm. We provide recommendation on selecting the type of parallel algorithm and its parameters in order to achieve the most efficient results for each class of instances.
ISSN:1045-9219
1558-2183
DOI:10.1109/TPDS.2025.3563849