Abstract
In the Max k-Edge-Colored Clustering problem (abbreviated as MAX-k-EC) we are given an undirected graph and k colors. Each edge of the graph has a color and a nonnegative weight. The goal is to color the vertices so as to maximize the total weight of the edges whose colors coincide with the colors of their endpoints. The problem was introduced by Angel et al. [3]. In this paper we give a polynomial-time algorithm for MAX-k-EC with an approximation factor \(\frac{4225}{11664}\approx 0.3622\) which significantly improves the best previously known approximation bound \(\frac{49}{144}\approx 0.3402\) established by Alhamdan and Kononov [2].
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Acknowledgments
The authors thank the anonymous referees for their helpful comments and suggestions. A. Ageev was supported by Program no. I.5.1 of Fundamental Research of the Siberian Branch of the Russian Academy of Sciences (project no. 0314-2019-0019). A. Kononov was supported by RFBR, project number 20-07-00458.
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Ageev, A., Kononov, A. (2020). A 0.3622-Approximation Algorithm for the Maximum k-Edge-Colored Clustering Problem. In: Kochetov, Y., Bykadorov, I., Gruzdeva, T. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2020. Communications in Computer and Information Science, vol 1275. Springer, Cham. https://doi.org/10.1007/978-3-030-58657-7_1
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DOI: https://doi.org/10.1007/978-3-030-58657-7_1
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