A Tighter Lower Bound for Optimal Bin Packing (original) (raw)

In this paper, we present an efficient algorithm to compute a tighter lower bound for the one-dimensional bin packing problem. The time complexity of the algorithm is O(n log n). We have simulated the algorithm on randomly generated bin packing problems with item sizes drawn uniformly from (a; b], 0 a ! b B. If our lower bound is used, on average, the error of BFD is less than 2%. For a + b B, the error is less than 0.003%. Key words: bin packing, lower bound, best fit decreasing, harmonic partition, matching. i 1 Introduction For NP-complete problems, it may not be possible to find optimal solutions in polynomial time. The quality of an approximation algorithm A is often measured by its asymptotic performance ratio [3] or worst-case performance ratio [6]. For an instance L of a minimization problem Pi, let S (L) be the optimal solution and A(L) be the solution obtained by using algorithm A. If a quantity implicitly depends on the problem instance L, then we drop L from our...