3,524 research outputs found
Hybrid next-fit algorithm for the two-dimensional rectangle bin-packing problem
We present a new approximation algorithm for the two-dimensional bin-packing problem. The algorithm is based on two one-dimensional bin-packing algorithms. Since the algorithm is of next-fit type it can also be used for those cases where the output is required to be on-line (e. g. if we open an new bin we have no possibility to pack elements into the earlier opened bins). We give a tight bound for its worst-case and show that this bound is a parameter of the maximal sizes of the items to be packed. Moreover, we also present a probabilistic analysis of this algorithm.worst-case analysis;probabilistic analysis;bin-packing;heuristic algorithm;on-line algorithm;two-dimensional packing
Hybrid next-fit algorithm for the two-dimensional rectangle bin-packing problem
We present a new approximation algorithm for the two-dimensional bin-packing problem. The algorithm is based on two one-dimensional bin-packing algorithms. Since the algorithm is of next-fit type it can also be used for those cases where the output is required to be on-line (e. g. if we open an new bin we have no possibility to pack elements into the earlier opened bins). We give a tight bound for its worst-case and show that this bound is a parameter of the maximal sizes of the items to be packed. Moreover, we also present a probabilistic analysis of this algorithm
SLO-aware Colocation of Data Center Tasks Based on Instantaneous Processor Requirements
In a cloud data center, a single physical machine simultaneously executes
dozens of highly heterogeneous tasks. Such colocation results in more efficient
utilization of machines, but, when tasks' requirements exceed available
resources, some of the tasks might be throttled down or preempted. We analyze
version 2.1 of the Google cluster trace that shows short-term (1 second) task
CPU usage. Contrary to the assumptions taken by many theoretical studies, we
demonstrate that the empirical distributions do not follow any single
distribution. However, high percentiles of the total processor usage (summed
over at least 10 tasks) can be reasonably estimated by the Gaussian
distribution. We use this result for a probabilistic fit test, called the
Gaussian Percentile Approximation (GPA), for standard bin-packing algorithms.
To check whether a new task will fit into a machine, GPA checks whether the
resulting distribution's percentile corresponding to the requested service
level objective, SLO is still below the machine's capacity. In our simulation
experiments, GPA resulted in colocations exceeding the machines' capacity with
a frequency similar to the requested SLO.Comment: Author's version of a paper published in ACM SoCC'1
Probabilistic analysis of algorithms for dual bin packing problems
In the dual bin packing problem, the objective is to assign items of given size to the largest possible number of bins, subject to the constraint that the total size of the items assigned to any bin is at least equal to 1. We carry out a probabilistic analysis of this problem under the assumption that the items are drawn independently from the uniform distribution on [0, 1] and reveal the connection between this problem and the classical bin packing problem as well as to renewal theory.
Recommended from our members
Packing items from a triangular distribution
We consider the problem of packing n items which are drawn according to a probability distribution whose density function is triangular in shape. For triangles which represent density functions whose expectation is 1/p for p = 3, 4, 5, ..., we give a packing strategy for which the ratio of the number of bins used in the packing to the expected total size of the items asymptotically approaches 1
Probabilistic alternatives for competitive analysis
In the last 20 years competitive analysis has become the main tool for analyzing the quality of online algorithms. Despite of this, competitive analysis has also been criticized: it sometimes cannot discriminate between algorithms that exhibit significantly different empirical behavior or it even favors an algorithm that is worse from an empirical point of view. Therefore, there have been several approaches to circumvent these drawbacks. In this survey, we discuss probabilistic alternatives for competitive analysis.operations research and management science;
Recommended from our members
An average-case analysis of bin packing with uniformly distributed item sizes
We analyze the one-dimensional bin-packing problem under the assumption that bins have unit capacity, and that items to be packed are drawn from a uniform distribution on [0,1]. Building on some recent work by Frederickson, we give an algorithm which uses n/2+0(n^½) bins on the average to pack n items. (Knodel has achieved a similar result.) The analysis involves the use of a certain 1-dimensional random walk. We then show that even an optimum packing under this distribution uses n/2+0(n^1/2) bins on the average, so our algorithm is asymptotically optimal, up to constant factors on the amount of wasted space. Finally, following Frederickson, we show that two well-known greedy bin-packing algorithms use no more bins than our algorithm; thus their behavior is also in asymptotically optimal in this sense
Recommended from our members
RGFGA: An efficient representation and crossover for grouping genetic algorithms
There is substantial research into genetic algorithms that are used to group large numbers of
objects into mutually exclusive subsets based upon some fitness function. However, nearly all
methods involve degeneracy to some degree.
We introduce a new representation for grouping genetic algorithms, the restricted growth function
genetic algorithm, that effectively removes all degeneracy, resulting in a more efficient search. A new crossover operator is also described that exploits a measure of similarity between chromosomes in a population. Using several synthetic datasets, we compare the performance of our representation and crossover with another well known state-of-the-art GA method, a strawman
optimisation method and a well-established statistical clustering algorithm, with encouraging results
- …