Suppose we sequentially put n balls into n bins. If we put each ball into a random bin then the heaviest bin will contain ∼ logn/ log logn balls with high probability. However, Azar, Broder, Karlin and Upfal [SIAM J. Comput. 29 (1999) 180–200] showed that if each time we choose two bins at random and put the ball in the least loaded bin among the two, then the heaviest bin will contain only ∼ l...

Bin packing is a well-known NP-Hard optimization problem which has several real applications. Classical bin packing (BPP) is a simple model where all bins are identical. However, the variable sized bin packing problem (VSBPP) is a generalization of the bin packing problem where bins of different capacities are available for packing a set of items having different weights. The objective is to pa...

We consider a generalized one-dimensional bin packing model in which the cost of a bin is a nondecreasing concave function of the utilization of the bin. We show that for any given positive constant , there exists a polynomial-time approximation algorithmwith an asymptotic worst-case performance ratio of no more than 1 + .

A study was undertaken to investigate the effect of liquid nitrogen aeration on mortalities of adult Cryptolestes furrugineus, rusty grain beetles, in a prototype cardboard grain bin equipped with an aeration system. The grain bin was filled with Hard Red Spring wheat and liquid nitrogen was introduced from the bottom of the bin. The survival of both cold acclimated and unacclimated C. furrugin...

MsatAllele is a computer package built on R to visualize and bin the raw microsatellite allele size distributions. The method is based on the creation of an R database with exported files from the open-source electropherogram peak-reading program STRAND. Contrary to other binning programs, in this program, the bin limits are not fixed and are automatically defined by the data stored in the data...

By jointly analyzing multiple variants within a gene together, instead of one at a time, gene-based regression analysis can improve power and robustness of genetic association analysis. Extending prior work that examined multi-bin linear combination (MLC) statistics for combined analysis of rare and common variants, here we investigate analysis of common variants more extensively under realisti...

Usually, for bin packing problems, we try to minimize the number of bins used or in the case of the dual bin packing problem, maximize the number of accepted items or accepted volume. This paper presents results for the opposite problems, where we want to maximize the number of bins used or minimize the number of accepted items or the accepted volume. For the off-line variant, we require that t...

Nowadays certain actions are taken to improve the level of cleanliness in the country. People are getting more active in doing all the things possible to clean their surroundings. Various movements are also started by the government to increase cleanliness. We will try to build a system which will notify the corporations to empty the bin on time. In this system, we will put a sensor on top of t...

The bin packing problem is to find the minimum number of bins of size one to pack a list of items with sizes a1, . . . , an in (0, 1]. Using uniform sampling, which selects a random element from the input list each time, we develop a randomized O( n)(log log n) ∑n i=1 ai +( 1 2 ) 1 2 ) time (1+2)approximation scheme for the bin packing problem. We show that every randomized algorithm with unifo...

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...