Approximating Bin Packing within O(log OPT · Log Log OPT) Bins
Approximating Bin Packing within O(log OPT · Log Log OPT) Bins
For bin packing, the input consists of n items with sizes s_1,...,s_n in [0,1] which have to be assigned to a minimum number of bins of size 1. The seminal Karmarkar-Karp algorithm from '82 produces a solution with at most OPT + O(log^2 OPT) bins. We provide the first improvement in now 3 decades and show that one can find a solution of cost OPT + O(log OPT * log log OPT) in polynomial time. This is achieved by rounding a fractional solution to the Gilmore-Gomory LP relaxation using the Entropy Method from discrepancy theory. The result is constructive via algorithms of Bansal and Lovett-Meka.
- Massachusetts Institute of Technology United States
FOS: Computer and information sciences, Computer Science - Data Structures and Algorithms, FOS: Mathematics, Mathematics - Combinatorics, Data Structures and Algorithms (cs.DS), Combinatorics (math.CO)
FOS: Computer and information sciences, Computer Science - Data Structures and Algorithms, FOS: Mathematics, Mathematics - Combinatorics, Data Structures and Algorithms (cs.DS), Combinatorics (math.CO)
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