1,052 research outputs found
Metrical Service Systems with Multiple Servers
We study the problem of metrical service systems with multiple servers
(MSSMS), which generalizes two well-known problems -- the -server problem,
and metrical service systems. The MSSMS problem is to service requests, each of
which is an -point subset of a metric space, using servers, with the
objective of minimizing the total distance traveled by the servers.
Feuerstein initiated a study of this problem by proving upper and lower
bounds on the deterministic competitive ratio for uniform metric spaces. We
improve Feuerstein's analysis of the upper bound and prove that his algorithm
achieves a competitive ratio of . In the randomized
online setting, for uniform metric spaces, we give an algorithm which achieves
a competitive ratio , beating the deterministic lower
bound of . We prove that any randomized algorithm for
MSSMS on uniform metric spaces must be -competitive. We then
prove an improved lower bound of on
the competitive ratio of any deterministic algorithm for -MSSMS, on
general metric spaces. In the offline setting, we give a pseudo-approximation
algorithm for -MSSMS on general metric spaces, which achieves an
approximation ratio of using servers. We also prove a matching
hardness result, that a pseudo-approximation with less than servers is
unlikely, even for uniform metric spaces. For general metric spaces, we
highlight the limitations of a few popular techniques, that have been used in
algorithm design for the -server problem and metrical service systems.Comment: 18 pages; accepted for publication at COCOON 201
On the Benefit of Virtualization: Strategies for Flexible Server Allocation
Virtualization technology facilitates a dynamic, demand-driven allocation and
migration of servers. This paper studies how the flexibility offered by network
virtualization can be used to improve Quality-of-Service parameters such as
latency, while taking into account allocation costs. A generic use case is
considered where both the overall demand issued for a certain service (for
example, an SAP application in the cloud, or a gaming application) as well as
the origins of the requests change over time (e.g., due to time zone effects or
due to user mobility), and we present online and optimal offline strategies to
compute the number and location of the servers implementing this service. These
algorithms also allow us to study the fundamental benefits of dynamic resource
allocation compared to static systems. Our simulation results confirm our
expectations that the gain of flexible server allocation is particularly high
in scenarios with moderate dynamics
Online Algorithms for Geographical Load Balancing
It has recently been proposed that Internet energy costs, both monetary and environmental, can be reduced by exploiting temporal variations and shifting processing to data centers located in regions where energy currently has low cost. Lightly loaded data centers can then turn off surplus servers. This paper studies online algorithms for determining the number of servers to leave on in each data center, and then uses these algorithms to study the environmental potential of geographical load balancing (GLB). A commonly suggested algorithm for this setting is “receding horizon control” (RHC), which computes the provisioning for the current time by optimizing over a window of predicted future loads. We show that RHC performs well in a homogeneous setting, in which all servers can serve all jobs equally well; however, we also prove that differences in propagation delays, servers, and electricity prices can cause RHC perform badly, So, we introduce variants of RHC that are guaranteed to perform as well in the face of such heterogeneity. These algorithms are then used to study the feasibility of powering a continent-wide set of data centers mostly by renewable sources, and to understand what portfolio of renewable energy is most effective
Ramsey-type theorems for metric spaces with applications to online problems
A nearly logarithmic lower bound on the randomized competitive ratio for the
metrical task systems problem is presented. This implies a similar lower bound
for the extensively studied k-server problem. The proof is based on Ramsey-type
theorems for metric spaces, that state that every metric space contains a large
subspace which is approximately a hierarchically well-separated tree (and in
particular an ultrametric). These Ramsey-type theorems may be of independent
interest.Comment: Fix an error in the metadata. 31 pages, 0 figures. Preliminary
version in FOCS '01. To be published in J. Comput. System Sc
Mixing predictions for online metric algorithms
A major technique in learning-augmented online algorithms is combining
multiple algorithms or predictors. Since the performance of each predictor may
vary over time, it is desirable to use not the single best predictor as a
benchmark, but rather a dynamic combination which follows different predictors
at different times. We design algorithms that combine predictions and are
competitive against such dynamic combinations for a wide class of online
problems, namely, metrical task systems. Against the best (in hindsight)
unconstrained combination of predictors, we obtain a competitive ratio
of , and show that this is best possible. However, for a benchmark
with slightly constrained number of switches between different predictors, we
can get a -competitive algorithm. Moreover, our algorithms can be
adapted to access predictors in a bandit-like fashion, querying only one
predictor at a time. An unexpected implication of one of our lower bounds is a
new structural insight about covering formulations for the -server problem
Software product description
An overview of the MultiNet system is presented. Services, supported configurations, remote printer services, netstat, netcontrol, DECnet interoperability services, and programming libraries are briefly described
The generalized work function algorithm is competitive for the generalized 2-server problem
The generalized 2-server problem is an online optimization problem where a
sequence of requests has to be served at minimal cost. Requests arrive one by
one and need to be served instantly by at least one of two servers. We consider
the general model where the cost function of the two servers may be different.
Formally, each server moves in its own metric space and a request consists of
one point in each metric space. It is served by moving one of the two servers
to its request point. Requests have to be served without knowledge of the
future requests. The objective is to minimize the total traveled distance. The
special case where both servers move on the real line is known as the
CNN-problem. We show that the generalized work function algorithm is constant
competitive for the generalized 2-server problem
Mixing predictions for online metric algorithms
A major technique in learning-augmented online algorithms is combining multiple algorithms or predictors. Since the performance of each predictor may vary over time, it is desirable to use not the single best predictor as a benchmark, but rather a dynamic combination which follows different predictors at different times. We design algorithms that combine predictions and are competitive against such dynamic combinations for a wide class of online problems, namely, metrical task systems. Against the best (in hindsight) unconstrained combination of ℓ predictors, we obtain a competitive ratio of (ℓ2), and show that this is best possible. However, for a benchmark with slightly constrained number of switches between different predictors, we can get a (1+)-competitive algorithm. Moreover, our algorithms can be adapted to access predictors in a bandit-like fashion, querying only one predictor at a time. An unexpected implication of one of our lower bounds is a new structural insight about covering formulations for the -server problem
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