research-article

Fast local search for the steiner problem in graphs

Authors:

Renato F. WerneckAuthors Info & Claims

Journal of Experimental Algorithmics (JEA), Volume 17

Article No.: 2.2, Pages 2.1 - 2.22

https://doi.org/10.1145/2133803.2184448

Published: 22 May 2012 Publication History

Abstract

We present efficient algorithms that implement four local searches for the Steiner problem in graphs: vertex insertion, vertex elimination, key-path exchange, and key-vertex elimination. In each case, we show how to find an improving solution (or prove that none exists in the neighborhood) in <it>O</it>(<it>m</it> log <it>n</it>) time on graphs with <it>n</it> vertices and <it>m</it> edges. Many of the techniques and data structures we use are relevant in the study of dynamic graphs in general, beyond Steiner trees. Besides the theoretical interest, our results have practical impact: These local searches have been shown to find good-quality solutions in practice, but high running times limited their applicability.

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Cited By

Shi YHan CGuo T(2024)NeuroPrim: An attention-based model for solving NP-hard spanning tree problemsScience China Mathematics10.1007/s11425-022-2175-567:6(1359-1376)Online publication date: 22-Feb-2024
https://doi.org/10.1007/s11425-022-2175-5
Yang BZheng W(2024)A Powerful Local Search Method for Minimum Steiner Tree ProblemWeb and Big Data10.1007/978-981-97-7241-4_4(50-66)Online publication date: 28-Aug-2024
https://doi.org/10.1007/978-981-97-7241-4_4
Wu XZhou Y(2022)A Fast Heuristic Algorithm for the Steiner Tree Problem with Uniform Edge Weights2022 5th International Conference on Pattern Recognition and Artificial Intelligence (PRAI)10.1109/PRAI55851.2022.9904263(1281-1286)Online publication date: 19-Aug-2022
https://doi.org/10.1109/PRAI55851.2022.9904263
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Published In

cover image ACM Journal of Experimental Algorithmics

ACM Journal of Experimental Algorithmics Volume 17, Issue

2012

427 pages

ISSN:1084-6654

EISSN:1084-6654

DOI:10.1145/2133803

Issue’s Table of Contents

Copyright © 2012 ACM.

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Publication History

Published: 22 May 2012

Published in JEA Volume 17

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Cited By

Shi YHan CGuo T(2024)NeuroPrim: An attention-based model for solving NP-hard spanning tree problemsScience China Mathematics10.1007/s11425-022-2175-567:6(1359-1376)Online publication date: 22-Feb-2024
https://doi.org/10.1007/s11425-022-2175-5
Yang BZheng W(2024)A Powerful Local Search Method for Minimum Steiner Tree ProblemWeb and Big Data10.1007/978-981-97-7241-4_4(50-66)Online publication date: 28-Aug-2024
https://doi.org/10.1007/978-981-97-7241-4_4
Wu XZhou Y(2022)A Fast Heuristic Algorithm for the Steiner Tree Problem with Uniform Edge Weights2022 5th International Conference on Pattern Recognition and Artificial Intelligence (PRAI)10.1109/PRAI55851.2022.9904263(1281-1286)Online publication date: 19-Aug-2022
https://doi.org/10.1109/PRAI55851.2022.9904263
Fichte JHecher MSchidler A(2020)Solving the Steiner Tree Problem with few Terminals2020 IEEE 32nd International Conference on Tools with Artificial Intelligence (ICTAI)10.1109/ICTAI50040.2020.00054(293-300)Online publication date: Nov-2020
https://doi.org/10.1109/ICTAI50040.2020.00054
Ljubić I(2020)Solving Steiner trees: Recent advances, challenges, and perspectivesNetworks10.1002/net.2200577:2(177-204)Online publication date: 27-Nov-2020
https://doi.org/10.1002/net.22005
Fu ZChen SMing YChen YLai X(2019)Dynamically Reconstructing Minimum Spanning Trees After Swapping Pairwise VerticesIEEE Access10.1109/ACCESS.2019.28948297(16351-16363)Online publication date: 2019
https://doi.org/10.1109/ACCESS.2019.2894829
Zhang HYe D(2018)Key-node-based local search discrete artificial bee colony algorithm for obstacle-avoiding rectilinear Steiner tree constructionNeural Computing and Applications10.1007/s00521-014-1760-426:4(875-898)Online publication date: 27-Dec-2018
https://dl.acm.org/doi/10.1007/s00521-014-1760-4
Brach PCygan MŁącki JSankowski P(2016)Algorithmic complexity of power law networksProceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms10.5555/2884435.2884526(1306-1325)Online publication date: 10-Jan-2016
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Zhang HYe DGuo W(2016)A Steiner point candidate-based heuristic framework for the Steiner tree problem in graphsJournal of Algorithms & Computational Technology10.1177/174830181664071410:2(99-114)Online publication date: 19-Apr-2016
https://doi.org/10.1177/1748301816640714

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