45,516 research outputs found
Optimal Placement Algorithms for Virtual Machines
Cloud computing provides a computing platform for the users to meet their
demands in an efficient, cost-effective way. Virtualization technologies are
used in the clouds to aid the efficient usage of hardware. Virtual machines
(VMs) are utilized to satisfy the user needs and are placed on physical
machines (PMs) of the cloud for effective usage of hardware resources and
electricity in the cloud. Optimizing the number of PMs used helps in cutting
down the power consumption by a substantial amount.
In this paper, we present an optimal technique to map virtual machines to
physical machines (nodes) such that the number of required nodes is minimized.
We provide two approaches based on linear programming and quadratic programming
techniques that significantly improve over the existing theoretical bounds and
efficiently solve the problem of virtual machine (VM) placement in data
centers
Intermittent predictive control of an inverted pendulum
Intermittent predictive pole-placement control is successfully applied to the constrained-state control of a prestabilised experimental inverted pendulum
Three isoparametric solid elements for NASTRAN
Linear, quadratic, and cubic isoparametric hexahedral solid elements have been added to the element library of NASTRAN. These elements are available for static, dynamic, buckling, and heat-transfer analyses. Because the isoparametric element matrices are generated by direct numerical integration over the volume of the element, variations in material properties, temperatures, and stresses within the elements are represented in the computations. In order to compare the accuracy of the new elements, three similar models of a slender cantilever were developed, one for each element. All elements performed well. As expected, however, the linear element model yielded excellent results only when shear behavior predominated. In contrast, the results obtained from the quadratic and cubic element models were excellent in both shear and bending
Decay rate estimations for linear quadratic optimal regulators
Let be the optimal control of the open-loop system
in a linear quadratic optimization problem. By using
different complex variable arguments, we give several lower and upper estimates
of the exponential decay rate of the closed-loop system .
Main attention is given to the case of a skew-Hermitian matrix .
Given an operator , for a class of cases, we find a matrix that
provides an almost optimal decay rate.
We show how our results can be applied to the problem of optimizing the decay
rate for a large finite collection of control systems , , and illustrate this on an example of a concrete mechanical system. At the
end of the article, we pose several questions concerning the decay rates in the
context of linear quadratic optimization and in a more general context of the
pole placement problem.Comment: 25 pages, 1 figur
Generalized Opinion Dynamics from Local Optimization Rules
We study generalizations of the Hegselmann-Krause (HK) model for opinion
dynamics, incorporating features and parameters that are natural components of
observed social systems. The first generalization is one where the strength of
influence depends on the distance of the agents' opinions. Under this setup, we
identify conditions under which the opinions converge in finite time, and
provide a qualitative characterization of the equilibrium. We interpret the HK
model opinion update rule as a quadratic cost-minimization rule. This enables a
second generalization: a family of update rules which possess different
equilibrium properties. Subsequently, we investigate models in which a external
force can behave strategically to modulate/influence user updates. We consider
cases where this external force can introduce additional agents and cases where
they can modify the cost structures for other agents. We describe and analyze
some strategies through which such modulation may be possible in an
order-optimal manner. Our simulations demonstrate that generalized dynamics
differ qualitatively and quantitatively from traditional HK dynamics.Comment: 20 pages, under revie
A Scalable Approach for Service Chain (SC) Mapping with Multiple SC Instances in a Wide-Area Network
Network Function Virtualization (NFV) aims to simplify deployment of network
services by running Virtual Network Functions (VNFs) on commercial
off-the-shelf servers. Service deployment involves placement of VNFs and
in-sequence routing of traffic flows through VNFs comprising a Service Chain
(SC). The joint VNF placement and traffic routing is called SC mapping. In a
Wide-Area Network (WAN), a situation may arise where several traffic flows,
generated by many distributed node pairs, require the same SC; then, a single
instance (or occurrence) of that SC might not be enough. SC mapping with
multiple SC instances for the same SC turns out to be a very complex problem,
since the sequential traversal of VNFs has to be maintained while accounting
for traffic flows in various directions. Our study is the first to deal with
the problem of SC mapping with multiple SC instances to minimize network
resource consumption. We first propose an Integer Linear Program (ILP) to solve
this problem. Since ILP does not scale to large networks, we develop a
column-generation-based ILP (CG-ILP) model. However, we find that exact
mathematical modeling of the problem results in quadratic constraints in our
CG-ILP. The quadratic constraints are made linear but even the scalability of
CG-ILP is limited. Hence, we also propose a two-phase column-generation-based
approach to get results over large network topologies within reasonable
computational times. Using such an approach, we observe that an appropriate
choice of only a small set of SC instances can lead to a solution very close to
the minimum bandwidth consumption. Further, this approach also helps us to
analyze the effects of number of VNF replicas and number of NFV nodes on
bandwidth consumption when deploying these minimum number of SC instances.Comment: arXiv admin note: substantial text overlap with arXiv:1704.0671
Fast Hierarchical Clustering and Other Applications of Dynamic Closest Pairs
We develop data structures for dynamic closest pair problems with arbitrary
distance functions, that do not necessarily come from any geometric structure
on the objects. Based on a technique previously used by the author for
Euclidean closest pairs, we show how to insert and delete objects from an
n-object set, maintaining the closest pair, in O(n log^2 n) time per update and
O(n) space. With quadratic space, we can instead use a quadtree-like structure
to achieve an optimal time bound, O(n) per update. We apply these data
structures to hierarchical clustering, greedy matching, and TSP heuristics, and
discuss other potential applications in machine learning, Groebner bases, and
local improvement algorithms for partition and placement problems. Experiments
show our new methods to be faster in practice than previously used heuristics.Comment: 20 pages, 9 figures. A preliminary version of this paper appeared at
the 9th ACM-SIAM Symp. on Discrete Algorithms, San Francisco, 1998, pp.
619-628. For source code and experimental results, see
http://www.ics.uci.edu/~eppstein/projects/pairs
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