1,173 research outputs found
Decentralized Constraint Satisfaction
We show that several important resource allocation problems in wireless
networks fit within the common framework of Constraint Satisfaction Problems
(CSPs). Inspired by the requirements of these applications, where variables are
located at distinct network devices that may not be able to communicate but may
interfere, we define natural criteria that a CSP solver must possess in order
to be practical. We term these algorithms decentralized CSP solvers. The best
known CSP solvers were designed for centralized problems and do not meet these
criteria. We introduce a stochastic decentralized CSP solver and prove that it
will find a solution in almost surely finite time, should one exist, also
showing it has many practically desirable properties. We benchmark the
algorithm's performance on a well-studied class of CSPs, random k-SAT,
illustrating that the time the algorithm takes to find a satisfying assignment
is competitive with stochastic centralized solvers on problems with order a
thousand variables despite its decentralized nature. We demonstrate the
solver's practical utility for the problems that motivated its introduction by
using it to find a non-interfering channel allocation for a network formed from
data from downtown Manhattan
An annotated overview of dynamic network flows
The need for more realistic network models led to the development of the dynamic network flow theory. In dynamic flow models it takes time for the flow to pass an arc, the flow can be delayed at nodes, and the network parameters, e.g., the arc capacities, can change in time. Surprisingly perhaps, despite being closer to reality, dynamic flow models have been overshadowed by the classical, static model. This is largely due to the fact that while very efficient solution methods exist for static flow problems, dynamic flow problems have proved to be more difficult to solve. Our purpose with this overview is to compensate for this eclipse and introduce dynamic flows to the interested reader. To this end, we present the main flow problems that can appear in a dynamic network, and review the literature for existing results about them. Our approach is solution oriented, as opposed to dealing with modelling issues. We intend to provide a survey that can be a first step for readers wondering whether a given dynamic network flow problem has been solved or not. Besides restating the problems, we also describe the main proposed solution methods. An additional feature of this paper is an annotated list of the most important references about the subject
On finding paths and flows in multicriteria, stochastic and time-varying networks
This dissertation addresses two classes of network flow problems in networks with multiple, stochastic and time-varying attributes. The first problem class is concerned with providing routing instructions with the ability to make updated decisions as information about travel conditions is revealed for individual travelers in a transportation network. Three exact algorithms are presented for identifying all or a subset of the adaptive Pareto-optimal solutions with respect to the expected value of each criterion from each node to a desired destination for each departure time in the period of interest.
The second problem class is concerned with problems of determining the optimal set of a priori path flows for evacuation in capacitated networks are addressed, where the time-dependent and stochastic nature of arc attributes and capacities inherent in these problems is explicitly considered. The concept of Safest Escape is formulated for developing egress instructions. An exact algorithm is proposed to determine the pattern of flow that maximizes the minimum path probability of successful arrival of supply at the sink.
While the Safest Escape problem considers stochastic, time-varying capacities, arc travel times, while time-varying, are deterministic quantities. Explicit consideration of stochastic and time-varying travel times makes the SEscape problem and other related problems significantly more difficult. A meta-heuristic based on the principles of genetic algorithms is developed for determining optimal path flows with respect to several problems in dynamic networks, where arc traversal times and capacities are random variables with probability mass functions that vary with time. The proposed genetic algorithm is extended for use in more difficult, stochastic, time-varying and multicriteria, capacitated networks, for which no exact, efficient algorithms exist. Several objectives may be simultaneously considered in determining the optimal flow pattern: minimize total time, maximize expected flow and maximize the minimum path probability of successful arrival at the sink (the objective of the SEscape problem). Numerical experiments are conducted to assess the performance of all proposed approaches
Maximum Likelihood Estimator for Hidden Markov Models in continuous time
The paper studies large sample asymptotic properties of the Maximum
Likelihood Estimator (MLE) for the parameter of a continuous time Markov chain,
observed in white noise. Using the method of weak convergence of likelihoods
due to I.Ibragimov and R.Khasminskii, consistency, asymptotic normality and
convergence of moments are established for MLE under certain strong ergodicity
conditions of the chain.Comment: Warning: due to a flaw in the publishing process, some of the
references in the published version of the article are confuse
Combinatorial Optimization
Combinatorial Optimization is an active research area that developed from the rich interaction among many mathematical areas, including combinatorics, graph theory, geometry, optimization, probability, theoretical computer science, and many others. It combines algorithmic and complexity analysis with a mature mathematical foundation and it yields both basic research and applications in manifold areas such as, for example, communications, economics, traffic, network design, VLSI, scheduling, production, computational biology, to name just a few. Through strong inner ties to other mathematical fields it has been contributing to and benefiting from areas such as, for example, discrete and convex geometry, convex and nonlinear optimization, algebraic and topological methods, geometry of numbers, matroids and combinatorics, and mathematical programming. Moreover, with respect to applications and algorithmic complexity, Combinatorial Optimization is an essential link between mathematics, computer science and modern applications in data science, economics, and industry
Electron-nuclear correlations for photo-induced dynamics in molecular dimers
Ultrafast photoinduced dynamics of electronic excitation in molecular dimers
is drastically affected by the dynamic reorganization of inter- and intra-
molecular nuclear configuration modeled by a quantized nuclear degree of
freedom [Cina et. al, J. Chem Phys. {118}, 46 (2003)]. The dynamics of the
electronic population and nuclear coherence is analyzed by solving the chain of
coupled differential equations for %mean coordinate, population inversion,
electron-vibrational correlation, etc. [Prezhdo, Pereverzev, J. Chem. Phys.
{113} 6557 (2000)]. Intriguing results are obtained in the approximation of a
small change of the nuclear equilibrium upon photoexcitation. In the limiting
case of resonance between the electronic energy gap and the frequency of the
nuclear mode these results are justified by comparison to the exactly solvable
Jaynes-Cummings model. It is found that the photoinduced processes in the model
dimer are arranged according to their time scales: (i) fast scale of nuclear
motion, (ii) intermediate scale of dynamical redistribution of electronic
population between excited states as well as growth and dynamics of
electron-nuclear correlation, (iii) slow scale of electronic population
approach to the quasi-equilibrium distribution, decay of electron-nuclear
correlation, and decrease of the amplitude of mean coordinate oscillation. The
latter processes are accompanied by a noticeable growth of the nuclear
coordinate dispersion associated with the overall nuclear wavepacket width. The
demonstrated quantum relaxation features of the photoinduced vibronic dynamics
in molecular dimers are obtained by a simple method, applicable to systems with
many degrees of freedom
Control of transport dynamics in overlay networks
Transport control is an important factor in the performance of Internet protocols, particularly in the next generation network applications involving computational steering, interactive visualization, instrument control, and transfer of large data sets. The widely deployed Transport Control Protocol is inadequate for these tasks due to its performance drawbacks. The purpose of this dissertation is to conduct a rigorous analytical study on the design and performance of transport protocols, and systematically develop a new class of protocols to overcome the limitations of current methods. Various sources of randomness exist in network performance measurements due to the stochastic nature of network traffic. We propose a new class of transport protocols that explicitly accounts for the randomness based on dynamic stochastic approximation methods. These protocols use congestion window and idle time to dynamically control the source rate to achieve transport objectives. We conduct statistical analyses to determine the main effects of these two control parameters and their interaction effects. The application of stochastic approximation methods enables us to show the analytical stability of the transport protocols and avoid pre-selecting the flow and congestion control parameters. These new protocols are successfully applied to transport control for both goodput stabilization and maximization. The experimental results show the superior performance compared to current methods particularly for Internet applications. To effectively deploy these protocols over the Internet, we develop an overlay network, which resides at the application level to provide data transmission service using User Datagram Protocol. The overlay network, together with the new protocols based on User Datagram Protocol, provides an effective environment for implementing transport control using application-level modules. We also study problems in overlay networks such as path bandwidth estimation and multiple quickest path computation. In wireless networks, most packet losses are caused by physical signal losses and do not necessarily indicate network congestion. Furthermore, the physical link connectivity in ad-hoc networks deployed in unstructured areas is unpredictable. We develop the Connectivity-Through-Time protocols that exploit the node movements to deliver data under dynamic connectivity. We integrate this protocol into overlay networks and present experimental results using network to support a team of mobile robots
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