Abstract
Graph matching is one of the most well-studied problems in combinatorial optimization. The history of the maximum weight matching problem, which is one of the most popular problems in graph matching, is intertwined with the development of modern graph theory. To solve this problem, Edmonds proposed the blossom algorithm. After that, an increasing number of approximation matching algorithms that can be faster in matching than the blossom algorithm has been proposed. However, matched weights should be considered. This study aims to improve the efficiency of solving the maximum weight matching algorithm by using clustering. Improving efficiency means achieving optimal matching while improving the running time. In this experiment, we attempt to use various real-world datasets to ensure the accuracy of experiments.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Hitchcock, F.L.: The distribution of a product from several sources to numerous localities. J. Math. Phys. 20(1–4), 224–230 (1941)
Thorndike, R.L.: The problem of classification of personnel. Psychometrika 15(3), 215–235 (1950)
Chan, P., Huang, X., Liu, Z., Zhang, C., Zhang, S.: Assignment and pricing in roommate market. In: Proceedings of the AAAI Conference on Artificial Intelligence. vol. 30 (2016)
Irving, R.W.: An efficient algorithm for the ‘stable roommates’ problem. J. Algor. 6(4), 577–595 (1985)
Zhao, B., Xu, P., Shi, Y., Tong, Y., Zhou, Z., Zeng, Y.: Preference-aware task assignment in on-demand taxi dispatching: an online stable matching approach. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 33, pp. 2245–2252 (2019)
Kujansuu, E., Lindberg, T., M’akinen, E.: The stable roommates problem and chess tournament pairings. Divulgaciones Matemáticas 7(1), 19–28 (1999)
Roth, A.E., Sönmez, T., Ünver, M.U.: Pairwise kidney exchange. J. Econ. Theory 125(2), 151–188 (2005)
Edmonds, J.: Paths, trees, and flowers. Can. J. Math. 17, 449–467 (1965)
Preis, R.: Linear time 1/2-approximation algorithm for maximum weighted matching in general graphs. STACS 99, 259–269 (1999)
Drake, D.E., Hougardy, S.: A simple approximation algorithm for the weighted matching problem. Inform. Process. Lett. 85(4), 211–213 (2003)
Drake, D.E., Hougardy, S.: Improved linear time approximation algorithms for weighted matchings. In: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, pp. 14–23 (2003)
Duan, R., Pettie, S.: Approximating maximum weight matching in near-linear time. In: 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, pp. 673–682 (2010)
Koana, T., Korenwein, V., Nichterlein, A., Zschoche, P.: Data reduction for maximum matching on real-world graphs: theory and experiments (2018). arXiv preprint
Wøhlk, S., Laporte, G.: Computational comparison of several greedy algorithms for the minimum cost perfect matching problem on large graphs. Comput. Oper. Res. 87, 107–113 (2017)
von Luxburg, U.: A tutorial on spectral clustering. Statist. Comput. 17(4), 395–416 (2007)
Shi, J., Malik, J.: Normalized cuts and image segmentation. In: Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 22, no. 8, pp. 888–905 (2000)
Wu, Z., Leahy, R.: An optimal graph theoretic approach to data clustering: theory and its application to image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 15(11), 1101–1113 (1993)
Sarkar, S., Soundararajan, P.: Supervised learning of large perceptual organization: graph spectral partitioning and learning automata. IEEE Trans. Pattern Anal. Mach. Intell. 22(5), 504–525 (2000)
Hagen, L., Kahng, A.B.: New spectral methods for ratio cut partitioning and clustering. IEEE Trans. Computer Aided Design Integr. Circ. Syst. 11(9), 1074–1085 (1992)
Blondel, V.D., Guillaume, J.L., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. J. Statist. Mech. Theory Experim. 2008, 10 (2008)
Clauset, A., Newman, M.E., Moore, C.: Finding community structure in very large networks. Phys. Rev. E 70, 6 (2004)
Newman, M.E., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69, 2 (2004)
Leskovec, J., Mcauley, J.: Learning to discover social circles in ego networks. In: Pereira, F., Burges, C.J.C., Bottou, L., Weinberger, K.Q. (eds.) Advances in Neural Information Processing Systems. vol. 25. Curran Associates, Inc. (2012). https://proceedings.neurips.cc/paper/2012/file/7a614fd06c325499f1680b9896beedeb-Paper.pdf
Rozemberczki, B., Davies, R., R.S., Sutton, C.: Gemsec: Graph embedding with self clustering. In: Proceedings of the IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, pp. 65–72 (2019)
Rozemberczki, B.C.A., Sarkar, R.: Multi-scale attributed node embedding (2019). arXiv preprint
Rozemberczki, B., Sarkar, R.: Characteristic functions on graphs: birds of a feather, from statistical descriptors to parametric models. In: Proceedings of the 29th ACM International Conference on Information & Knowledge Management, pp. 1325–1334 (2020)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
He, L., Saga, R. (2022). Heuristic Approach to Improve the Efficiency of Maximum Weight Matching Algorithm Using Clustering. In: Czarnowski, I., Howlett, R.J., Jain, L.C. (eds) Intelligent Decision Technologies. Smart Innovation, Systems and Technologies, vol 309. Springer, Singapore. https://doi.org/10.1007/978-981-19-3444-5_3
Download citation
DOI: https://doi.org/10.1007/978-981-19-3444-5_3
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-19-3443-8
Online ISBN: 978-981-19-3444-5
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)