The k-constrained bipartite matching problem: approximation algorithms and applications to wireless networks

  • Authors:

  • André Berger;James Gross;Tobias Harks

  • Affiliations:

  • Department of Quantitative Economics, Maastricht University, The Netherlands;UMIC Research Centre, RWTH Aachen University, Germany;Institute of Mathematics, Technical University Berlin, Germany

  • Venue:
  • INFOCOM'10 Proceedings of the 29th conference on Information communications
  • Year:
  • 2010

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Abstract

In communication networks, resource assignment problems appear in several different settings. These problems are often modeled by a maximum weight matching problem in bipartite graphs and efficient matching algorithms are well known. In several applications, the corresponding matching problem has to be solved many times in a row as the underlying system operates in a time-slotted fashion and the edge weights change over time. However, changing the assignments can come with a certain cost for reconfiguration that depends on the number of changed edges between subsequent assignments. In order to control the cost of reconfiguration, we propose the k-constrained bipartite matching problem for bipartite graphs, which seeks an optimal matching that realizes at most k changes from a previous matching. We provide fast approximation algorithms with provable guarantees for this problem. Furthermore, to cope with the sequential nature of assignment problems, we introduce an online variant of the k- constrained matching problem and derive online algorithms that are based on our approximation algorithms for the k-constrained bipartite matching problem. Finally, we establish the applicability of our model and our algorithms in the context of OFDMA wireless networks finding a significant performance improvement for the proposed algorithms.