7,180 research outputs found
Locality-preserving allocations Problems and coloured Bin Packing
We study the following problem, introduced by Chung et al. in 2006. We are
given, online or offline, a set of coloured items of different sizes, and wish
to pack them into bins of equal size so that we use few bins in total (at most
times optimal), and that the items of each colour span few bins (at
most times optimal). We call such allocations -approximate. As usual in bin packing problems, we allow additive
constants and consider as the asymptotic performance ratios.
We prove that for \eps>0, if we desire small , no scheme can beat
(1+\eps, \Omega(1/\eps))-approximate allocations and similarly as we desire
small , no scheme can beat (1.69103, 1+\eps)-approximate allocations.
We give offline schemes that come very close to achieving these lower bounds.
For the online case, we prove that no scheme can even achieve
-approximate allocations. However, a small restriction on item
sizes permits a simple online scheme that computes (2+\eps, 1.7)-approximate
allocations
Online Bin Covering with Limited Migration
Semi-online models where decisions may be revoked in a limited way have been studied extensively in the last years.
This is motivated by the fact that the pure online model is often too restrictive to model real-world applications, where some changes might be allowed. A well-studied measure of the amount of decisions that can be revoked is the migration factor beta: When an object o of size s(o) arrives, the decisions for objects of total size at most beta * s(o) may be revoked. Usually beta should be a constant. This means that a small object only leads to small changes. This measure has been successfully investigated for different, classical problems such as bin packing or makespan minimization. The dual of makespan minimization - the Santa Claus or machine covering problem - has also been studied, whereas the dual of bin packing - the bin covering problem - has not been looked at from such a perspective.
In this work, we extensively study the bin covering problem with migration in different scenarios. We develop algorithms both for the static case - where only insertions are allowed - and for the dynamic case, where items may also depart. We also develop lower bounds for these scenarios both for amortized migration and for worst-case migration showing that our algorithms have nearly optimal migration factor and asymptotic competitive ratio (up to an arbitrary small epsilon). We therefore resolve the competitiveness of the bin covering problem with migration
A tight lower bound for an online hypercube packing problem and bounds for prices of anarchy of a related game
We prove a tight lower bound on the asymptotic performance ratio of
the bounded space online -hypercube bin packing problem, solving an open
question raised in 2005. In the classic -hypercube bin packing problem, we
are given a sequence of -dimensional hypercubes and we have an unlimited
number of bins, each of which is a -dimensional unit hypercube. The goal is
to pack (orthogonally) the given hypercubes into the minimum possible number of
bins, in such a way that no two hypercubes in the same bin overlap. The bounded
space online -hypercube bin packing problem is a variant of the
-hypercube bin packing problem, in which the hypercubes arrive online and
each one must be packed in an open bin without the knowledge of the next
hypercubes. Moreover, at each moment, only a constant number of open bins are
allowed (whenever a new bin is used, it is considered open, and it remains so
until it is considered closed, in which case, it is not allowed to accept new
hypercubes). Epstein and van Stee [SIAM J. Comput. 35 (2005), no. 2, 431-448]
showed that is and , and conjectured that
it is . We show that is in fact . To
obtain this result, we elaborate on some ideas presented by those authors, and
go one step further showing how to obtain better (offline) packings of certain
special instances for which one knows how many bins any bounded space algorithm
has to use. Our main contribution establishes the existence of such packings,
for large enough , using probabilistic arguments. Such packings also lead to
lower bounds for the prices of anarchy of the selfish -hypercube bin packing
game. We present a lower bound of for the pure price of
anarchy of this game, and we also give a lower bound of for
its strong price of anarchy
Multi-capacity bin packing with dependent items and its application to the packing of brokered workloads in virtualized environments
Providing resource allocation with performance
predictability guarantees is increasingly important in cloud
platforms, especially for data-intensive applications, in which
performance depends greatly on the available rates of data
transfer between the various computing/storage hosts underlying
the virtualized resources assigned to the application. Existing
resource allocation solutions either assume that applications
manage their data transfer between their virtualized resources, or
that cloud providers manage their internal networking resources.
With the increased prevalence of brokerage services in cloud
platforms, there is a need for resource allocation solutions that
provides predictability guarantees in settings, in which neither
application scheduling nor cloud provider resources can be
managed/controlled by the broker. This paper addresses this
problem, as we define the Network-Constrained Packing (NCP)
problem of finding the optimal mapping of brokered resources
to applications with guaranteed performance predictability. We
prove that NCP is NP-hard, and we define two special instances
of the problem, for which exact solutions can be found efficiently.
We develop a greedy heuristic to solve the general instance of the
NCP problem , and we evaluate its efficiency using simulations
on various application workloads, and network models.This work was done while author was at Boston University. It was partially supported by NSF CISE awards #1430145, #1414119, #1239021 and #1012798. (1430145 - NSF CISE; 1414119 - NSF CISE; 1239021 - NSF CISE; 1012798 - NSF CISE
Performance-oriented Cloud Provisioning: Taxonomy and Survey
Cloud computing is being viewed as the technology of today and the future.
Through this paradigm, the customers gain access to shared computing resources
located in remote data centers that are hosted by cloud providers (CP). This
technology allows for provisioning of various resources such as virtual
machines (VM), physical machines, processors, memory, network, storage and
software as per the needs of customers. Application providers (AP), who are
customers of the CP, deploy applications on the cloud infrastructure and then
these applications are used by the end-users. To meet the fluctuating
application workload demands, dynamic provisioning is essential and this
article provides a detailed literature survey of dynamic provisioning within
cloud systems with focus on application performance. The well-known types of
provisioning and the associated problems are clearly and pictorially explained
and the provisioning terminology is clarified. A very detailed and general
cloud provisioning classification is presented, which views provisioning from
different perspectives, aiding in understanding the process inside-out. Cloud
dynamic provisioning is explained by considering resources, stakeholders,
techniques, technologies, algorithms, problems, goals and more.Comment: 14 pages, 3 figures, 3 table
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