Almost optimal solutions for bin coloring problems

Authors:
Mingen Lin;Zhiyong Lin;Jinhui Xu
Affiliations:
Department of Computer Science and Engineering, University at Buffalo, the State University of New York, Buffalo, NY;Department of Computer Science and Engineering, University at Buffalo, the State University of New York, Buffalo, NY;Department of Computer Science and Engineering, University at Buffalo, the State University of New York, Buffalo, NY
Venue:
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Year:
2005

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Abstract

In this paper we study two interesting bin coloring problems: Minimum Bin Coloring Problem (MinBC) and Online Maximum Bin Coloring Problem (OMaxBC), motivated from several applications in networking. For the MinBC problem, we first show that it is NP-complete, and then present two near linear time approximation algorithms to achieve almost optimal solutions, i.e., no more than OPT+2 and OPT+1 respectively, where OPT is the optimal solution. For the OMaxBC problem, we first introduce a deterministic 2-competitive greedy algorithm, and then give lower bounds for any deterministic and randomized (against adaptive offline adversary) online algorithms. The lower bounds show that our deterministic algorithm achieves the best possible competitive ratio.