NETEMBED: A Network Resource Mapping Service for Distributed Applications

Emerging configurable infrastructures such as large-scale overlays and grids, distributed testbeds, and sensor networks comprise diverse sets of available computing resources (e.g., CPU and OS capabilities and memory constraints) and network conditions (e.g., link delay, bandwidth, loss rate, and jitter) whose characteristics are both complex and time-varying. At the same time, distributed applications to be deployed on these infrastructures exhibit increasingly complex constraints and requirements on resources they wish to utilize. Examples include selecting nodes and links to schedule an overlay multicast file transfer across the Grid, or embedding a network experiment with specific resource constraints in a distributed testbed such as PlanetLab. Thus, a common problem facing the efficient deployment of distributed applications on these infrastructures is that of "mapping" application-level requirements onto the network in such a manner that the requirements of the application are realized, assuming that the underlying characteristics of the network are known. We refer to this problem as the network embedding problem. In this paper, we propose a new approach to tackle this combinatorially-hard problem. Thanks to a number of heuristics, our approach greatly improves performance and scalability over previously existing techniques. It does so by pruning large portions of the search space without overlooking any valid embedding. We present a construction that allows a compact representation of candidate embeddings, which is maintained by carefully controlling the order via which candidate mappings are inserted and invalid mappings are removed. We present an implementation of our proposed technique, which we call NETEMBED – a service that identify feasible mappings of a virtual network configuration (the query network) to an existing real infrastructure or testbed (the hosting network). We present results of extensive performance evaluation experiments of NETEMBED using several combinations of real and synthetic network topologies. Our results show that our NETEMBED service is quite effective in identifying one (or all) possible embeddings for quite sizable queries and hosting networks – much larger than what any of the existing techniques or services are able to handle.National Science Foundation (CNS Cybertrust 0524477, NSF CNS NeTS 0520166, NSF CNS ITR 0205294, EIA RI 0202067

Combinatorial Optimization

This report summarizes the meeting on Combinatorial Optimization where new and promising developments in the field were discussed. Th

Algebraic and Geometric Models for Space Networking

In this paper we introduce some new algebraic and geometric perspectives on networked space communications. Our main contribution is a novel definition of a time-varying graph (TVG), defined in terms of a matrix with values in subsets of the real line P(R). We leverage semi-ring properties of P(R) to model multi-hop communication in a TVG using matrix multiplication and a truncated Kleene star. This leads to novel statistics on the communication capacity of TVGs called lifetime curves, which we generate for large samples of randomly chosen STARLINK satellites, whose connectivity is modeled over day-long simulations. Determining when a large subsample of STARLINK is temporally strongly connected is further analyzed using novel metrics introduced here that are inspired by topological data analysis (TDA). To better model networking scenarios between the Earth and Mars, we introduce various semi-rings capable of modeling propagation delay as well as protocols common to Delay Tolerant Networking (DTN), such as store-and-forward. Finally, we illustrate the applicability of zigzag persistence for featurizing different space networks and demonstrate the efficacy of K-Nearest Neighbors (KNN) classification for distinguishing Earth-Mars and Earth-Moon satellite systems using time-varying topology alone.Comment: 43 pages, 18 figures, comments welcom

Approximation and Control of Skill Based Parallel Service Systems with Homogeneous Service

A skill base parallel service system is comprised of a set of customers of different classes that arrive randomly for service, a set of servers that serve those customers and a set of qualifications that defines which customer classes can be served by which server. Systems of this kind appear in a wide range of applications from the assignment of jobs to employees with different skills to network traffic routing. Literature regarding these systems has almost exclusively been focused on the asymptotic heavy traffic regime. The reason being that such an asymptotic regime is convenient to analyze and allows the derivation of exact results. However, although many applications can be well approximated by an asymptotic regime, many others can not. In this work we are especially concerned with large scale sparse systems where, despite the system being large of scale, each customer class can only be served by a small subset of the servers. After laying foundations for the model in Chapter 1 and exploring structural properties in Chapter 2 we go on to present the two main contributions of this work. In Chapter 3 we develop a set of approximations that compile to a , first of its kind, approximation scheme of matching rates of skill based parallel service system operating under the \textit{first-come-first-serve} or \textit{longest-queue-first} policies. The accuracy of the approximation is verified with extensive simulation experiments where it is shown to provide matching rate estimates with an absolute error of $3\%-5\%$ for a wide range of traffic intensities. Later, in Chapter 4 we use insights provided by the new approximation to derive weighted versions of the \textit{first-come-first-serve} or \textit{longest-queue-first} and show, through comprehensive simulation testing, that these weighted polices dramatically reduce the waiting time of customers in congested system compared to the original unweighted versions. Finally, we extend the use of the weighted policies to systems with matching rewards and show that, by appropriate choice of weights, these policies can be used by a controller to efficiently trade-off between the rate of reward accumulation and waiting time experienced by the customer

Low-variance black-box gradient estimates for the Plackett-Luce distribution

Learning models with discrete latent variables using stochastic gradient descent remains a challenge due to the high variance of gradient estimates. Modern variance reduction techniques mostly consider categorical distributions and have limited applicability when the number of possible outcomes becomes large. In this work, we consider models with latent permutations and propose control variates for the Plackett-Luce distribution. In particular, the control variates allow us to optimize black-box functions over permutations using stochastic gradient descent. To illustrate the approach, we consider a variety of causal structure learning tasks for continuous and discrete data. We show that our method outperforms competitive relaxation-based optimization methods and is also applicable to non-differentiable score functions

Design and Optimization in Near-term Quantum Computation

Quantum computers have come a long way since conception, and there is still a long way to go before the dream of universal, fault-tolerant computation is realized. In the near term, quantum computers will occupy a middle ground that is popularly known as the “Noisy, Intermediate-Scale Quantum” (or NISQ) regime. The NISQ era represents a transition in the nature of quantum devices from experimental to computational. There is significant interest in engineering NISQ devices and NISQ algorithms in a manner that will guide the development of quantum computation in this regime and into the era of fault-tolerant quantum computing. In this thesis, we study two aspects of near-term quantum computation. The first of these is the design of device architectures, covered in Chapters 2, 3, and 4. We examine different qubit connectivities on the basis of their graph properties, and present numerical and analytical results on the speed at which large entangled states can be created on nearest-neighbor grids and graphs with modular structure. Next, we discuss the problem of permuting qubits among the nodes of the connectivity graph using only local operations, also known as routing. Using a fast quantum primitive to reverse the qubits in a chain, we construct a hybrid, quantum/classical routing algorithm on the chain. We show via rigorous bounds that this approach is faster than any SWAP-based algorithm for the same problem. The second part, which spans the final three chapters, discusses variational algorithms, which are a class of algorithms particularly suited to near-term quantum computation. Two prototypical variational algorithms, quantum adiabatic optimization (QAO) and the quantum approximate optimization algorithm (QAOA), are studied for the difference in their control strategies. We show that on certain crafted problem instances, bang-bang control (QAOA) can be as much as exponentially faster than quasistatic control (QAO). Next, we demonstrate the performance of variational state preparation on an analog quantum simulator based on trapped ions. We show that using classical heuristics that exploit structure in the variational parameter landscape, one can find circuit parameters efficiently in system size as well as circuit depth. In the experiment, we approximate the ground state of a critical Ising model with long-ranged interactions on up to 40 spins. Finally, we study the performance of Local Tensor, a classical heuristic algorithm inspired by QAOA on benchmarking instances of the MaxCut problem, and suggest physically motivated choices for the algorithm hyperparameters that are found to perform well empirically. We also show that our implementation of Local Tensor mimics imaginary-time quantum evolution under the problem Hamiltonian

Kronecker Graphs: An Approach to Modeling Networks

How can we model networks with a mathematically tractable model that allows for rigorous analysis of network properties? Networks exhibit a long list of surprising properties: heavy tails for the degree distribution; small diameters; and densification and shrinking diameters over time. Most present network models either fail to match several of the above properties, are complicated to analyze mathematically, or both. In this paper we propose a generative model for networks that is both mathematically tractable and can generate networks that have the above mentioned properties. Our main idea is to use the Kronecker product to generate graphs that we refer to as "Kronecker graphs". First, we prove that Kronecker graphs naturally obey common network properties. We also provide empirical evidence showing that Kronecker graphs can effectively model the structure of real networks. We then present KronFit, a fast and scalable algorithm for fitting the Kronecker graph generation model to large real networks. A naive approach to fitting would take super- exponential time. In contrast, KronFit takes linear time, by exploiting the structure of Kronecker matrix multiplication and by using statistical simulation techniques. Experiments on large real and synthetic networks show that KronFit finds accurate parameters that indeed very well mimic the properties of target networks. Once fitted, the model parameters can be used to gain insights about the network structure, and the resulting synthetic graphs can be used for null- models, anonymization, extrapolations, and graph summarization

An extensive English language bibliography on graph theory and its applications

Bibliography on graph theory and its application