1,960 research outputs found
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
Limitations of quantum computing with Gaussian cluster states
We discuss the potential and limitations of Gaussian cluster states for
measurement-based quantum computing. Using a framework of Gaussian projected
entangled pair states (GPEPS), we show that no matter what Gaussian local
measurements are performed on systems distributed on a general graph, transport
and processing of quantum information is not possible beyond a certain
influence region, except for exponentially suppressed corrections. We also
demonstrate that even under arbitrary non-Gaussian local measurements, slabs of
Gaussian cluster states of a finite width cannot carry logical quantum
information, even if sophisticated encodings of qubits in continuous-variable
(CV) systems are allowed for. This is proven by suitably contracting tensor
networks representing infinite-dimensional quantum systems. The result can be
seen as sharpening the requirements for quantum error correction and fault
tolerance for Gaussian cluster states, and points towards the necessity of
non-Gaussian resource states for measurement-based quantum computing. The
results can equally be viewed as referring to Gaussian quantum repeater
networks.Comment: 13 pages, 7 figures, details of main argument extende
Generating Representative ISP Technologies From First-Principles
Understanding and modeling the factors that underlie the growth and evolution of network topologies are basic questions that impact capacity planning, forecasting, and protocol research. Early topology generation work focused on generating network-wide connectivity maps, either at the AS-level or the router-level, typically with an eye towards reproducing abstract properties of observed topologies. But recently, advocates of an alternative "first-principles" approach question the feasibility of realizing representative topologies with simple generative models that do not explicitly incorporate real-world constraints, such as the relative costs of router configurations, into the model. Our work synthesizes these two lines by designing a topology generation mechanism that incorporates first-principles constraints. Our goal is more modest than that of constructing an Internet-wide topology: we aim to generate representative topologies for single ISPs. However, our methods also go well beyond previous work, as we annotate these topologies with representative capacity and latency information. Taking only demand for network services over a given region as input, we propose a natural cost model for building and interconnecting PoPs and formulate the resulting optimization problem faced by an ISP. We devise hill-climbing heuristics for this problem and demonstrate that the solutions we obtain are quantitatively similar to those in measured router-level ISP topologies, with respect to both topological properties and fault-tolerance
Unfaithful Glitch Propagation in Existing Binary Circuit Models
We show that no existing continuous-time, binary value-domain model for
digital circuits is able to correctly capture glitch propagation. Prominent
examples of such models are based on pure delay channels (P), inertial delay
channels (I), or the elaborate PID channels proposed by Bellido-D\'iaz et al.
We accomplish our goal by considering the solvability/non-solvability border of
a simple problem called Short-Pulse Filtration (SPF), which is closely related
to arbitration and synchronization. On one hand, we prove that SPF is solvable
in bounded time in any such model that provides channels with non-constant
delay, like I and PID. This is in opposition to the impossibility of solving
bounded SPF in real (physical) circuit models. On the other hand, for binary
circuit models with constant-delay channels, we prove that SPF cannot be solved
even in unbounded time; again in opposition to physical circuit models.
Consequently, indeed none of the binary value-domain models proposed so far
(and that we are aware of) faithfully captures glitch propagation of real
circuits. We finally show that these modeling mismatches do not hold for the
weaker eventual SPF problem.Comment: 23 pages, 15 figure
Fault Tolerant Gradient Clock Synchronization
Synchronizing clocks in distributed systems is well-understood, both in terms
of fault-tolerance in fully connected systems and the dependence of local and
global worst-case skews (i.e., maximum clock difference between neighbors and
arbitrary pairs of nodes, respectively) on the diameter of fault-free systems.
However, so far nothing non-trivial is known about the local skew that can be
achieved in topologies that are not fully connected even under a single
Byzantine fault. Put simply, in this work we show that the most powerful known
techniques for fault-tolerant and gradient clock synchronization are
compatible, in the sense that the best of both worlds can be achieved
simultaneously.
Concretely, we combine the Lynch-Welch algorithm [Welch1988] for
synchronizing a clique of nodes despite up to Byzantine faults with
the gradient clock synchronization (GCS) algorithm by Lenzen et al.
[Lenzen2010] in order to render the latter resilient to faults. As this is not
possible on general graphs, we augment an input graph by
replacing each node by fully connected copies, which execute an instance
of the Lynch-Welch algorithm. We then interpret these clusters as supernodes
executing the GCS algorithm, where for each cluster its correct nodes'
Lynch-Welch clocks provide estimates of the logical clock of the supernode in
the GCS algorithm. By connecting clusters corresponding to neighbors in
in a fully bipartite manner, supernodes can inform each other
about (estimates of) their logical clock values. This way, we achieve
asymptotically optimal local skew, granted that no cluster contains more than
faulty nodes, at factor and overheads in terms of nodes and
edges, respectively. Note that tolerating faulty neighbors trivially
requires degree larger than , so this is asymptotically optimal as well
Quantum Communication and Decoherence
In this contribution we will give a brief overview on the methods used to
overcome decoherence in quantum communication protocols. We give an
introduction to quantum error correction, entanglement purification and quantum
cryptography. It is shown that entanglement purification can be used to create
``private entanglement'', which makes it a useful tool for cryptographic
protocols.Comment: 31 pages, 10 figures, LaTeX, book chapter to appear in ``Coherent
Evolution in Noisy Environments'', Lecture Notes in Physics, (Springer
Verlag, Berlin-Heidelberg-New York). Minor typos correcte
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