Abstract
In parallel computation domain, graph coloring is widely studied in its own and represents a reference problem for scheduling of parallel tasks. Unfortunately, common graph coloring strategies usually focus on minimizing the number of colors without any concern for the sizes of each color class, thus producing highly skewed color class distributions. However, to guarantee efficiency in parallel computations, but also in other application contexts, it is important to keep the color classes highly balanced in their sizes. In this paper we address this challenging issue for large scale graphs, proposing a fast parallel MCMC heuristic for sparse graphs that randomly generates good balanced colorings provided that a sufficient number of colors are made available. We show its effectiveness through some numerical simulations on random graphs.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Boman, E.G., Bozdağ, D., Catalyurek, U., Gebremedhin, A.H., Manne, F.: A scalable parallel graph coloring algorithm for distributed memory computers. In: Cunha, J.C., Medeiros, P.D. (eds.) Euro-Par 2005. LNCS, vol. 3648, pp. 241–251. Springer, Heidelberg (2005). https://doi.org/10.1007/11549468_29
Coleman, T.F., Moré, J.J.: Estimation of sparse Jacobian matrices and graph coloring problems. SIAM J. Numer. Anal. 20(1), 187–209 (1983)
Comi, P., et al.: Hardware-accelerated high-resolution video coding in virtual network functions. In: European Conference on Networks and Communications (EuCNC), pp. 32–36 (2016)
Cuculo, V., Lanzarotti, R., Boccignone, G.: Using sparse coding for landmark localization in facial expressions. In: 5th European Workshop on Visual Information Processing, EUVIP 2014, pp. 1–6. IEEE (2014)
Erdős, P., Rènyi, A.: On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci. 5, 17–61 (1960)
Fakhraei, S., Foulds, J., Shashanka, M., Getoor, L.: Collective spammer detection in evolving multi-relational social networks. In: Proceedings of 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1769–1778. ACM (2015)
Garey, M.R., Johnson, D.S.: Computers and Intractability; A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1990)
Gjertsen, R.K., Jones, M.T., Plassmann, P.E.: Parallel heuristics for improved, balanced graph colorings. J. Parallel Distrib. Comput. 37, 171–186 (1996)
Gómez, D., Montero, J., Yáñez, J.: A coloring fuzzy graph approach for image classification. Inf. Sci. 176(24), 3645–3657 (2006)
Hastings, W.: Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57(1), 97–109 (1970)
Janis, P., et al.: Device-to-device communication underlaying cellular communications systems. Int. J. Commun. Netw. Syst. Sci. 2(3), 169–178 (2009). ISSN 1913-3715
Jerrum, M.R.: A very simple algorithm for estimating the number of \(k\)-colourings of a low-degree graph. Random Struct. Algorithms 7, 157–165 (1995)
Jones, M.T., Plassmann, P.E.: A parallel graph coloring heuristic. SIAM J. Sci. Comput. 14, 654–669 (1992)
Lu, H., Halappanavar, M., Chavarria-Miranda, D., Gebremedhin, A., Kalyanaraman, A.: Balanced coloring for parallel computing applications. In: Proceedings of the IEEE 29th International Parallel and Distributed Processing Symposium, pp. 7–16 (2015)
Luby, M.: A simple parallel algorithm for the maximal independent set problem. In: Proceedings of the 17th Annual ACM Symposium on Theory of Computing, pp. 1–10 (1985)
Lupaşcu, C.A., Tegolo, D., Bellavia, F., Valenti, C.: Semi-automatic registration of retinal images based on line matching approach. In: Proceedings of the 26th IEEE International Symposium on Computer-Based Medical Systems, pp. 453–456. IEEE (2013)
Meer, P.: Stochastic image pyramids. CVGIP 45(3), 269–294 (1989)
Meyer, W.: Equitable coloring. Am. Math. Mon. 80, 920–922 (1973)
Mosa, M.A., Hamouda, A., Marei, M.: Graph coloring and aco based summarization for social networks. Expert. Syst. Appl. 74, 115–126 (2017)
Robert, J., Gjertsen, K., Jones, M.T., Plassmann, P.: Parallel heuristics for improved, balanced graph colorings. J. Parallel Distrib. Comput. 37, 171–186 (1996)
Tantipathananandh, C., Berger-Wolf, T., Kempe, D.: A framework for community identification in dynamic social networks. In: Proceedings of the 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 717–726. ACM (2007)
Tsolkas, D., Liotou, E., Passas, N., Merakos, L.: A graph-coloring secondary resource allocation for D2D communications in LTE networks. In: IEEE 17th International Workshop on Computer Aided Modeling and Design (CAMAD), pp. 56–60. IEEE (2012)
Voss, J.: An Introduction to Statistical Computing: A Simulation-based Approach. Wiley, Chichester (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Conte, D., Grossi, G., Lanzarotti, R., Lin, J., Petrini, A. (2019). A Parallel MCMC Algorithm for the Balanced Graph Coloring Problem. In: Conte, D., Ramel, JY., Foggia, P. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2019. Lecture Notes in Computer Science(), vol 11510. Springer, Cham. https://doi.org/10.1007/978-3-030-20081-7_16
Download citation
DOI: https://doi.org/10.1007/978-3-030-20081-7_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-20080-0
Online ISBN: 978-3-030-20081-7
eBook Packages: Computer ScienceComputer Science (R0)
