Bin packing can be solved within 1 + ε in linear time

Abstract

For any listL ofn numbers in (0, 1) letL* denote the minimum number of unit capacity bins needed to pack the elements ofL. We prove that, for every positive ε, there exists anO(n)-time algorithmS such that, ifS(L) denotes the number of bins used byS forL, thenS(L)/L*≦1+ε for anyL providedL* is sufficiently large.

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The work of this author was supported by NSF Grant MCS 70-04997.

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Fernandez de la Vega, W., Lueker, G.S. Bin packing can be solved within 1 + ε in linear time. Combinatorica 1, 349–355 (1981). https://doi.org/10.1007/BF02579456

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AMS subject classification (1980)

  • 68 C 25
  • 68 E 05
  • 90 C 10