The bin packing problem is one of the classical NP-hard optimization problems. In this paper, we present a simple generic approach for obtaining new fast lower bounds, based on dual feasible functions. Worst-case analysis as well as computational results show that one of our classes clearly outperforms the previous best “economical” lower bound for the bin packing problem by Martello and Toth, ...

Galambos, G. and J.B.G. Frenk, A simple proof of Liang’s lower bound for on-line bin packing and the extension to the parametric case, Discrete Applied Mathematics 41 (1993) 173-178. In this note we present a simplified proof of a lower bound for on-line bin packing. This proof also covers the well-known result given by Liang in Inform. Process Lett. 10 (1980) 76-79.

On-line algorithms have been extensively studied for the onedimensional bin packing problem. Semi-online property relax the online prescription in such a way that it allows some extra operations or the algorithm knows more (e.g. the optimum value) in advance. In this paper we present an improved lower bound for the asymptotic competitive ratio of any on-line bin packing algorithm which knows th...

We analyze the List scheduling algorithm for the problem of minimizing makespan using a worst-average-case or wac analysis technique, previously used by Kenyon for analyzing the Best Fit bin packing algorithm. We show that List’s worst-average-case or wac ratio asymptotically approaches 2 as m→∞. Thus, List’s worst-case behavior is not overly dependent on the order of job arrivals.

High efficiency orange OLEDs have been achieved using a trifunctional Pt(II) complex that contains an electron-transporting triarylborane and a hole-transporting triarylamine.

Abstract. In 1996 Ivkovič and Lloyd [A fundamental restriction on fully dynamic maintenance of bin packing, Inform. Process. Lett., 59 (1996), pp. 229–232] gave the lower bound 4 3 on the asymptotic worst-case ratio for so-called fully dynamic bin packing algorithms, where the number of repackable items in each step is restricted by a constant. In this paper we improve this result to about 1.38...

In this paper we establish a general algorithmic framework between bin packing and strip packing, with which we achieve the same asymptotic bounds by applying bin packing algorithms to strip packing. More precisely we obtain the following results: (1) Any offline bin packing algorithm can be applied to strip packing maintaining the same asymptotic worst-case ratio. Thus using FFD (MFFD) as a su...

In this paper we use the theory of computing to study fractal dimensions of projections in Euclidean spaces. A fundamental result in fractal geometry is Marstrands projection theorem, which shows that for every analytic set E, for almost every line L, the Hausdorff dimension of the orthogonal projection of E onto L is maximal. We use Kolmogorov complexity to give two new results on the Hausdorf...

In the bin packing problem we are given an instance consisting of a sequence of items with sizes between 0 and 1. The objective is to pack these items into the smallest possible number of bins of unit size. BestFit algorithm packs each item into the most full bin where it fits, possibly opening a new bin if the item cannot fit into any currently open bin. In early seventies it was shown that th...