7,995 research outputs found
Robust Fault Tolerant uncapacitated facility location
In the uncapacitated facility location problem, given a graph, a set of
demands and opening costs, it is required to find a set of facilities R, so as
to minimize the sum of the cost of opening the facilities in R and the cost of
assigning all node demands to open facilities. This paper concerns the robust
fault-tolerant version of the uncapacitated facility location problem (RFTFL).
In this problem, one or more facilities might fail, and each demand should be
supplied by the closest open facility that did not fail. It is required to find
a set of facilities R, so as to minimize the sum of the cost of opening the
facilities in R and the cost of assigning all node demands to open facilities
that did not fail, after the failure of up to \alpha facilities. We present a
polynomial time algorithm that yields a 6.5-approximation for this problem with
at most one failure and a 1.5 + 7.5\alpha-approximation for the problem with at
most \alpha > 1 failures. We also show that the RFTFL problem is NP-hard even
on trees, and even in the case of a single failure
Fault Tolerant Clustering Revisited
In discrete k-center and k-median clustering, we are given a set of points P
in a metric space M, and the task is to output a set C \subseteq ? P, |C| = k,
such that the cost of clustering P using C is as small as possible. For
k-center, the cost is the furthest a point has to travel to its nearest center,
whereas for k-median, the cost is the sum of all point to nearest center
distances. In the fault-tolerant versions of these problems, we are given an
additional parameter 1 ?\leq \ell \leq ? k, such that when computing the cost
of clustering, points are assigned to their \ell-th nearest-neighbor in C,
instead of their nearest neighbor. We provide constant factor approximation
algorithms for these problems that are both conceptually simple and highly
practical from an implementation stand-point
Maximum gradient embeddings and monotone clustering
Let (X,d_X) be an n-point metric space. We show that there exists a
distribution D over non-contractive embeddings into trees f:X-->T such that for
every x in X, the expectation with respect to D of the maximum over y in X of
the ratio d_T(f(x),f(y)) / d_X(x,y) is at most C (log n)^2, where C is a
universal constant. Conversely we show that the above quadratic dependence on
log n cannot be improved in general. Such embeddings, which we call maximum
gradient embeddings, yield a framework for the design of approximation
algorithms for a wide range of clustering problems with monotone costs,
including fault-tolerant versions of k-median and facility location.Comment: 25 pages, 2 figures. Final version, minor revision of the previous
one. To appear in "Combinatorica
Designing application software in wide area network settings
Progress in methodologies for developing robust local area network software has not been matched by similar results for wide area settings. The design of application software spanning multiple local area environments is examined. For important classes of applications, simple design techniques are presented that yield fault tolerant wide area programs. An implementation of these techniques as a set of tools for use within the ISIS system is described
Optimal Data Placement on Networks With Constant Number of Clients
We introduce optimal algorithms for the problems of data placement (DP) and
page placement (PP) in networks with a constant number of clients each of which
has limited storage availability and issues requests for data objects. The
objective for both problems is to efficiently utilize each client's storage
(deciding where to place replicas of objects) so that the total incurred access
and installation cost over all clients is minimized. In the PP problem an extra
constraint on the maximum number of clients served by a single client must be
satisfied. Our algorithms solve both problems optimally when all objects have
uniform lengths. When objects lengths are non-uniform we also find the optimal
solution, albeit a small, asymptotically tight violation of each client's
storage size by lmax where lmax is the maximum length of the objects
and some arbitrarily small positive constant. We make no assumption
on the underlying topology of the network (metric, ultrametric etc.), thus
obtaining the first non-trivial results for non-metric data placement problems
Unconstrained and Constrained Fault-Tolerant Resource Allocation
First, we study the Unconstrained Fault-Tolerant Resource Allocation (UFTRA)
problem (a.k.a. FTFA problem in \cite{shihongftfa}). In the problem, we are
given a set of sites equipped with an unconstrained number of facilities as
resources, and a set of clients with set as corresponding
connection requirements, where every facility belonging to the same site has an
identical opening (operating) cost and every client-facility pair has a
connection cost. The objective is to allocate facilities from sites to satisfy
at a minimum total cost. Next, we introduce the Constrained
Fault-Tolerant Resource Allocation (CFTRA) problem. It differs from UFTRA in
that the number of resources available at each site is limited by .
Both problems are practical extensions of the classical Fault-Tolerant Facility
Location (FTFL) problem \cite{Jain00FTFL}. For instance, their solutions
provide optimal resource allocation (w.r.t. enterprises) and leasing (w.r.t.
clients) strategies for the contemporary cloud platforms.
In this paper, we consider the metric version of the problems. For UFTRA with
uniform , we present a star-greedy algorithm. The algorithm
achieves the approximation ratio of 1.5186 after combining with the cost
scaling and greedy augmentation techniques similar to
\cite{Charikar051.7281.853,Mahdian021.52}, which significantly improves the
result of \cite{shihongftfa} using a phase-greedy algorithm. We also study the
capacitated extension of UFTRA and give a factor of 2.89. For CFTRA with
uniform , we slightly modify the algorithm to achieve
1.5186-approximation. For a more general version of CFTRA, we show that it is
reducible to FTFL using linear programming
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