Online Bin Packing with Resource Augmentation

Abstract

C e n t r u m v o o r W i s k u n d e e n I n f o r m a t i c aOnline Bin Packing with Resource Augmentation ABSTRACT In competitive analysis, we usually do not put any restrictions on the computational complexity of online algorithms, although efficient algorithms are preferred. Thus if such an algorithm were given the entire input in advance, it could give an optimal solution (in exponential time). Instead of giving the algorithm more knowledge about the input, in this paper we consider the effects of giving an online bin packing algorithm larger bins than the offline algorithm it is compared to. We give new algorithms for this problem that combine items in bins in an unusual way and give bounds on their performance which improve upon the best possible bounded space algorithm. We also give general lower bounds for this problem which are nearly matching for bin sizes b 2. AbstractIn competitive analysis, we usually do not put any restrictions on the computational complexity of online algorithms, although efficient algorithms are preferred. Thus if such an algorithm were given the entire input in advance, it could give an optimal solution (in exponential time). Instead of giving the algorithm more knowledge about the input, in this paper we consider the effects of giving an online bin packing algorithm larger bins than the offline algorithm it is compared to. We give new algorithms for this problem that combine items in bins in an unusual way and give bounds on their performance which improve upon the best possible bounded space algorithm. We also give general lower bounds for this problem which are nearly matching for bin sizes b ≥ 2.

Resource augmented semi-online bounded space bin packing

“…They gave on-line bounded space bin-packing algorithms for every b ≥ 1, whose worst case ratio in this model comes arbitrary close to the ρ(b) bound. Moreover, they proved that for every b ≥ 1 no on-line bounded space algorithm can perform better than ρ(b) in the worst case, thus showing that the optimal asymptotic competitive ratio for the on-line bounded space algorithms with resource augmentation b is a strictly decreasing function ρ(b) of b. Unbounded space resource augmented bin-packing was studied in [6].…”

“…We subtract the last inequality multiplied by 3 2 from (13). This yields B > 1 4 + β 6 . Finally, we plug in B ≤ β 3 (there are β B 2 -items, each of size smaller than 1…”

Competitive analysis of fundamental scheduling algorithms on a fault-prone machine and the impact of resource augmentation

“…For example, Johnson et al [16] analyze the worst-case performance of two simple algorithms (Best Fit and Next Fit) for the bin packing problem, giving upper bounds on the number of bins needed (corresponding to the completed time in our work). Epstein et al [17] (see also [15]) considered online bin packing with resource augmentation in the size of the bins (corresponding to the length of alive intervals in our work). Observe that the essential difference of the online bin packing problem with the one that we are looking at in this work, is that in our system the bins and their sizes (corresponding to the machine's alive intervals) are unknown.…”

On Dynamic Bin Packing: An Improved Lower Bound and Resource Augmentation Analysis

“…A natural question arises: Is packing items of restricted form, such as unit fraction items, as difficult as packing items of general form? Another aspect, resource augmentation analysis [16] has been studied in the context of on-line bin packing [12,13], in which an on-line algorithm can use bins of size b (>1) times that of the optimal off-line algorithm. To our knowledge, there is no previous work on resource augmentation analysis for dynamic bin packing.…”

“…Resource augmentation analysis for on-line bin packing has been studied [12,13]; matching upper and lower bounds (up to an additive constant) are given for bounded space bin packing [12] in which there is a limit on the number of opened bins that can be used at any time; and a better upper bound has been derived for (unbounded space) on-line bin packing [13]. Ivkovic and Lloyd studied the fully dynamic bin packing problem [15], which is a variant of dynamic bin packing that allows repacking of items for each item arrival or departure.…”