20,204 research outputs found
Network correlated data gathering with explicit communication: NP-completeness and algorithms
We consider the problem of correlated data gathering by a network with a sink node and a tree-based communication structure, where the goal is to minimize the total transmission cost of transporting the information collected by the nodes, to the sink node. For source coding of correlated data, we consider a joint entropy-based coding model with explicit communication where coding is simple and the transmission structure optimization is difficult. We first formulate the optimization problem definition in the general case and then we study further a network setting where the entropy conditioning at nodes does not depend on the amount of side information, but only on its availability. We prove that even in this simple case, the optimization problem is NP-hard. We propose some efficient, scalable, and distributed heuristic approximation algorithms for solving this problem and show by numerical simulations that the total transmission cost can be significantly improved over direct transmission or the shortest path tree. We also present an approximation algorithm that provides a tree transmission structure with total cost within a constant factor from the optimal
Networked Slepian-Wolf: theory, algorithms, and scaling laws
Consider a set of correlated sources located at the nodes of a network, and a set of sinks that are the destinations for some of the sources. The minimization of cost functions which are the product of a function of the rate and a function of the path weight is considered, for both the data-gathering scenario, which is relevant in sensor networks, and general traffic matrices, relevant for general networks. The minimization is achieved by jointly optimizing a) the transmission structure, which is shown to consist in general of a superposition of trees, and b) the rate allocation across the source nodes, which is done by Slepian-Wolf coding. The overall minimization can be achieved in two concatenated steps. First, the optimal transmission structure is found, which in general amounts to finding a Steiner tree, and second, the optimal rate allocation is obtained by solving an optimization problem with cost weights determined by the given optimal transmission structure, and with linear constraints given by the Slepian-Wolf rate region. For the case of data gathering, the optimal transmission structure is fully characterized and a closed-form solution for the optimal rate allocation is provided. For the general case of an arbitrary traffic matrix, the problem of finding the optimal transmission structure is NP-complete. For large networks, in some simplified scenarios, the total costs associated with Slepian-Wolf coding and explicit communication (conditional encoding based on explicitly communicated side information) are compared. Finally, the design of decentralized algorithms for the optimal rate allocation is analyzed
An efficient multi-core implementation of a novel HSS-structured multifrontal solver using randomized sampling
We present a sparse linear system solver that is based on a multifrontal
variant of Gaussian elimination, and exploits low-rank approximation of the
resulting dense frontal matrices. We use hierarchically semiseparable (HSS)
matrices, which have low-rank off-diagonal blocks, to approximate the frontal
matrices. For HSS matrix construction, a randomized sampling algorithm is used
together with interpolative decompositions. The combination of the randomized
compression with a fast ULV HSS factorization leads to a solver with lower
computational complexity than the standard multifrontal method for many
applications, resulting in speedups up to 7 fold for problems in our test
suite. The implementation targets many-core systems by using task parallelism
with dynamic runtime scheduling. Numerical experiments show performance
improvements over state-of-the-art sparse direct solvers. The implementation
achieves high performance and good scalability on a range of modern shared
memory parallel systems, including the Intel Xeon Phi (MIC). The code is part
of a software package called STRUMPACK -- STRUctured Matrices PACKage, which
also has a distributed memory component for dense rank-structured matrices
Irreversible Performance of a Quantum Harmonic Heat Engine
The unavoidable irreversible losses of power in a heat engine are found to be
of quantum origin. Following thermodynamic tradition a model quantum heat
engine operating by the Otto cycle is analyzed. The working medium of the model
is composed of an ensemble of harmonic oscillators. A link is established
between the quantum observables and thermodynamical variables based on the
concept of canonical invariance. These quantum variables are sufficient to
determine the state of the system and with it all thermodynamical variables.
Conditions for optimal work, power and entropy production show that maximum
power is a compromise between the quasistatic limit of adiabatic following on
the compression and expansion branches and a sudden limit of very short time
allocation to these branches. At high temperatures and quasistatic operating
conditions the efficiency at maximum power coincides with the endoreversible
result. The optimal compression ratio varies from the square root of the
temperature ratio in the quasistatic limit where their reversibility is
dominated by heat conductance to the temperature ratio to the power of 1/4 in
the sudden limit when the irreversibility is dominated by friction. When the
engine deviates from adiabatic conditions the performance is subject to
friction. The origin of this friction can be traced to the noncommutability of
the kinetic and potential energy of the working medium.Comment: 25 pages, 7 figures. Revision added explicit heat-transfer expression
and extended the discussion on the quantum origin of frictio
Optimal Orchestration of Virtual Network Functions
-The emergence of Network Functions Virtualization (NFV) is bringing a set of
novel algorithmic challenges in the operation of communication networks. NFV
introduces volatility in the management of network functions, which can be
dynamically orchestrated, i.e., placed, resized, etc. Virtual Network Functions
(VNFs) can belong to VNF chains, where nodes in a chain can serve multiple
demands coming from the network edges. In this paper, we formally define the
VNF placement and routing (VNF-PR) problem, proposing a versatile linear
programming formulation that is able to accommodate specific features and
constraints of NFV infrastructures, and that is substantially different from
existing virtual network embedding formulations in the state of the art. We
also design a math-heuristic able to scale with multiple objectives and large
instances. By extensive simulations, we draw conclusions on the trade-off
achievable between classical traffic engineering (TE) and NFV infrastructure
efficiency goals, evaluating both Internet access and Virtual Private Network
(VPN) demands. We do also quantitatively compare the performance of our VNF-PR
heuristic with the classical Virtual Network Embedding (VNE) approach proposed
for NFV orchestration, showing the computational differences, and how our
approach can provide a more stable and closer-to-optimum solution
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