We study on-line bounded space bin-packing in the resource augmentation model of competitive analysis. In this model, the on-line bounded space packing algorithm has to pack a list L of items with sizes in (0, 1], into a minimum number of bins of size b, b ≥ 1. A bounded space algorithm has the property that it only has a constant number of active bins available to accept items at any point dur...

An instance of the classical bin packing problem consists of a positive real C and a list L = (a1, a2, ..., an) of items with sizes 0 < s(ai) ≤ C, 1 ≤ i ≤ n; a solution to the problem is a partition of L into a minimum number of blocks, called bins, such that the sum of the sizes of the items in each bin is at most the capacity C. The capacity is just a scaling parameter; as is customary, we pu...

Mutual Information (MI) is a popular similarity measure for performing image registration between di↵erent modalities. MI makes a statistical comparison between two images by computing the entropy from the probability distribution of the data. Therefore, to obtain an accurate registration it is important to have an accurate estimation of the true underlying probability distribution. Within the ...

Mutual information (MI) is a popular similarity measure for performing image registration between different modalities. MI makes a statistical comparison between two images by computing the entropy from the probability distribution of the data. Therefore, to obtain an accurate registration it is important to have an accurate estimation of the true underlying probability distribution. Within the...

BACKGROUND Hepatocellular carcinoma is difficult to diagnose early, and most patients are already in the late stages of the disease when they are admitted to hospital. The total 5-year survival rate is less than 5%. Recent studies have showed that brucine has a good anti-tumor effect, but high toxicity, poor water solubility, short half-life, narrow therapeutic window, and a toxic dose that is ...

We introduce and study the batched bin packing problem (BBPP), a bin packing problem in which items become available for packing incrementally, one batch at a time. A batched algorithm must pack a batch before the next batch becomes known. A batch may contain several items; the special case when each batch consists of merely one item is the well-studied on-line bin packing problem. We obtain lo...

I suggest for memorization an equation for calculating approximate sample size requirements intended only for a specific set of values (80 per cent power for a two-tailed alpha = 0.05 test) which seems to occur often in biopharmaceutical research. After presenting the formula in terms of variance estimate s2 and effect size d, I derive a few alternative forms and then discuss the accuracy of th...

Following the work of Anily et al., we consider a variant of bin packing, called BIN PACKING WITH GENERAL COST STRUCTURES (GCBP) and design an asymptotic fully polynomial time approximation scheme (AFPTAS) for this problem. In the classic bin packing problem, a set of one-dimensional items is to be assigned to subsets of total size at most 1, that is, to be packed into unit sized bins. However,...

In this paper, we present an O(n1ogn) algorithm to compute a tighter lower bound for the one-dimensional bin packing problem. We have simulated the algorithm on randomly generated bin packing problems with item sizes drawn uniformly from (a, b], where 0 5 a < b 5 B and B is bin size. Using our lower bound, the average error of BFD is less than 2%. For a + b > B, the error is less than 0.003%. K...