Abstract
We consider the Max k-Edge-Colored Clustering problem (abbreviated as MAX-k-EC). We are given an edge-colored graph with k colors. Each edge of the graph has a positive weight. We seek to color the vertices of the graph so as to maximize the total weight of the edges which have the same color at their extremities. The problem was introduced by Angel et al. [2]. We give a polynomial-time algorithm for MAX-k-EC with an approximation factor \(\frac{\mathbf {49}}{\mathbf {144}}\approx 0.34,\) which significantly improves the best previously known factor \(\frac{\mathbf {7}}{\mathbf {23}}\approx 0.304,\) obtained by Ageev and Kononov [1]. We also present an upper bound of \(\frac{\mathbf {241}}{\mathbf {248}}\approx 0.972\) on the inapproximability of MAX-k-EC. This is the first inapproximability result for this problem.
This work was appeared as part of the first author’s MSc thesis.
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Alhamdan, Y.M., Kononov, A. (2019). Approximability and Inapproximability for Maximum k-Edge-Colored Clustering Problem. In: van Bevern, R., Kucherov, G. (eds) Computer Science – Theory and Applications. CSR 2019. Lecture Notes in Computer Science(), vol 11532. Springer, Cham. https://doi.org/10.1007/978-3-030-19955-5_1
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DOI: https://doi.org/10.1007/978-3-030-19955-5_1
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