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Clustering on k-Edge-Colored Graphs
Book chapter   Open access   Peer reviewed

Clustering on k-Edge-Colored Graphs

Eric Angel, Evripidis Bampis, Alexander Kononov, Dimitris Paparas, Emmanouil Pountourakis and Vassilis Zissimopoulos
Mathematical Foundations of Computer Science 2013, pp 50-61
2013
DOI: https://doi.org/10.1007/978-3-642-40313-2_7
url
http://www.cs.columbia.edu/%7Epaparas/clustering.pdfView
SubmittedOpen Access (License Unspecified),  Open

Abstract

Additional Color Adjacent Edge Bipartite Graph Initial Graph Matched Edge
We study the Max k-colored clustering problem, where, given an edge-colored graph with k colors, we seek to color the vertices of the graph so as to find a clustering of the vertices maximizing the number (or the weight) of matched edges, i.e. the edges having the same color as their extremities. We show that the cardinality problem is NP-hard even for edge-colored bipartite graphs with a chromatic degree equal to two and k ≥ 3. Our main result is a constant approximation algorithm for the weighted version of the Max k-colored clustering problem which is based on a rounding of a natural linear programming relaxation. For graphs with chromatic degree equal to two, we improve this ratio by exploiting the relation of our problem with the Max 2-and problem. We also present a reduction to the maximum-weight independent set (IS) problem in bipartite graphs which leads to a polynomial time algorithm for the case of two colors.

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