3UBC-Computer Science - Computer Science Department (UBC DEPARTMENT OF COMPUTER SCIENCE ICICS/CS Building 201-2366 Main Mall Vancouver, B.C. V6T 1Z4 General Enquiries: Tel: 604-822-3061 E-mail: info@cs.ubc.ca Fax: 604-822-5485 - Canada)
UBC - University of British Columbia (Vancouver Campus, , 2329 West Mall, Vancouver, BC Canada V6T 1Z4 -
Okanagan Campus, 3333 University Way, Kelowna, BC Canada V1V 1V7 - Canada)
4EECS department (633 Clark Street, Evanston, IL - United States)
5Communication Networks Laboratory [Athens] (Communication Networks Laboratory Department of Informatics and Telecommunications, University of Athens, Ilisia Campus (Panepistimiopolis), 157 84 Athens, Greece. - Greece)
Abstract : We study the Max kk-colored clustering problem, where given an edge-colored graph with kk 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≥3k≥3. Our main result is a constant approximation algorithm for the weighted version of the Max kk-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.
https://hal.archives-ouvertes.fr/hal-01366446
Contributor : Christoph Dürr
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Submitted on : Wednesday, September 14, 2016 - 3:49:05 PM
Last modification on : Monday, October 28, 2019 - 10:24:08 AM
