arXiv subjects

Stacy Patterson

Publications and source records attributed to Stacy Patterson.

At least 37 records · Page 2Linked to original sources

arXiv2021

Formal Guarantees of Timely Progress for Distributed Knowledge Propagation

Autonomous air traffic management (ATM) operations for urban air mobility (UAM) will necessitate the use of distributed protocols for decentralized coordination between aircraft. As UAM operations are time-critical, it will be imperative to have formal guarantees of progress for the distributed protocols used in ATM. Under asynchronous settings, message transmission and processing delays are unbounded, making it impossible to provide deterministic bounds on the time required to make progress. We present an approach for formally guaranteeing timely progress in a Two-Phase Acknowledge distributed knowledge propagation protocol by probabilistically modeling the delays using theories of the Multicopy Two-Hop Relay protocol and the M/M/1 queue system. The guarantee states a probabilistic upper bound to the time for progress as a function of the probabilities of the total transmission and processing delays being less than two given values. We also showcase the development of a library of formal theories, that is tailored towards reasoning about timely progress in distributed protocols deployed in airborne networks, in the Athena proof assistant.

cs.DC↗

arXiv2021

Verification of Eventual Consensus in Synod Using a Failure-Aware Actor Model

Successfully attaining consensus in the absence of a centralized coordinator is a fundamental problem in distributed multi-agent systems. We analyze progress in the Synod consensus protocol -- which does not assume a unique leader -- under the assumptions of asynchronous communication and potential agent failures. We identify a set of sufficient conditions under which it is possible to guarantee that a set of agents will eventually attain consensus. First, a subset of the agents must behave correctly and not permanently fail until consensus is reached, and second, at least one proposal must be eventually uninterrupted by higher-numbered proposals. To formally reason about agent failures, we introduce a failure-aware actor model (FAM). Using FAM, we model the identified conditions and provide a formal proof of eventual progress in Synod. Our proof has been mechanically verified using the Athena proof assistant and, to the best of our knowledge, it is the first machine-checked proof of eventual progress in Synod.

cs.DC↗

arXiv2021

Multi-Tier Federated Learning for Vertically Partitioned Data

We consider decentralized model training in tiered communication networks. Our network model consists of a set of silos, each holding a vertical partition of the data. Each silo contains a hub and a set of clients, with the silo's vertical data shard partitioned horizontally across its clients. We propose Tiered Decentralized Coordinate Descent (TDCD), a communication-efficient decentralized training algorithm for such two-tiered networks. To reduce communication overhead, the clients in each silo perform multiple local gradient steps before sharing updates with their hub. Each hub adjusts its coordinates by averaging its workers' updates, and then hubs exchange intermediate updates with one another. We present a theoretical analysis of our algorithm and show the dependence of the convergence rate on the number of vertical partitions, the number of local updates, and the number of clients in each hub. We further validate our approach empirically via simulation-based experiments using a variety of datasets and both convex and non-convex objectives.

cs.LG↗

arXiv2020

A Hierarchical Model for Fast Distributed Consensus in Dynamic Networks

We present two new consensus algorithms for dynamic networks. The first, Fast Raft, is a variation on the Raft consensus algorithm that reduces the number of message rounds in typical operation. Fast Raft is ideal for fast-paced distributed systems where membership changes over time and where sites must reach consensus quickly. The second, C-Raft, is targeted for distributed systems where sites are grouped into clusters, with fast communication within clusters and slower communication between clusters. C-Raft uses Fast Raft as a building block and defines a hierarchical model of consensus to improve upon throughput in globally distributed systems. We prove the safety and liveness properties of each algorithm. Finally, we present an experimental evaluation of both algorithms in AWS.

cs.DC↗

arXiv2020

Skedulix: Hybrid Cloud Scheduling for Cost-Efficient Execution of Serverless Applications

We present a framework for scheduling multifunction serverless applications over a hybrid public-private cloud. A set of serverless jobs is input as a batch, and the objective is to schedule function executions over the hybrid platform to minimize the cost of public cloud use, while completing all jobs by a specified deadline. As this scheduling problem is NP-Hard, we propose a greedy algorithm that dynamically determines both the order and placement of each function execution using predictive models of function execution time and network latencies. We present a prototype implementation of our framework that uses AWS Lambda and OpenFaaS, for the public and private cloud, respectively. We evaluate our prototype in live experiments using a mixture of compute and I/O heavy serverless applications. Our results show that our framework can achieve a speedup in batch processing of up to 1.92 times that of an approach that uses only the private cloud, at 40.5% the cost of an approach that uses only the public cloud.

cs.DC↗

arXiv2020

Performance Optimization for Edge-Cloud Serverless Platforms via Dynamic Task Placement

We present a framework for performance optimization in serverless edge-cloud platforms using dynamic task placement. We focus on applications for smart edge devices, for example, smart cameras or speakers, that need to perform processing tasks on input data in real to near-real time. Our framework allows the user to specify cost and latency requirements for each application task, and for each input, it determines whether to execute the task on the edge device or in the cloud. Further, for cloud executions, the framework identifies the container resource configuration needed to satisfy the performance goals. We have evaluated our framework in simulation using measurements collected from serverless applications in AWS Lambda and AWS Greengrass. In addition, we have implemented a prototype of our framework that runs in these same platforms. In experiments with our prototype, our models can predict average end-to-end latency with less than 6% error, and we obtain almost three orders of magnitude reduction in end-to-end latency compared to edge-only execution.

cs.DC↗

arXiv2020

Shifting Opinions in a Social Network Through Leader Selection

We study the French-DeGroot opinion dynamics in a social network with two polarizing parties. We consider a network in which the leaders of one party are given, and we pose the problem of selecting the leader set of the opposing party so as to shift the average opinion to a desired value. When each party has only one leader, we express the average opinion in terms of the transition matrix and the stationary distribution of random walks in the network. The analysis shows balance of influence between the two leader nodes. We show that the problem of selecting at most $k$ absolute leaders to shift the average opinion is $\mathbf{NP}$-hard. Then, we reduce the problem to a problem of submodular maximization with a submodular knapsack constraint and an additional cardinality constraint and propose a greedy algorithm with upper bound search to approximate the optimum solution. We also conduct experiments in random networks and real-world networks to show the effectiveness of the algorithm.

cs.SI↗

arXiv2020

Disagreement and Polarization in Two-Party Social Networks

We investigate disagreement and polarization in a social network with two polarizing sources of information. First, we define disagreement and polarization indices in two-party leader-follower models of opinion dynamics. We then give expressions for the indices in terms of a graph Laplacian. The expressions show a relationship between these quantities and the concepts of resistance distance and biharmonic distance. We next study the problem of designing the network so as to minimize disagreement and polarization. We give conditions for optimal disagreement and polarization, and further, we show that a linear combination of disagreement and polarization of the follower nodes is a convex function of the edge weights between followers. We propose algorithms to address some related continuous and discrete optimization problems and also present analytic results for some interesting examples.

cs.SI↗

arXiv2020

Diffusion and Consensus in a Weakly Coupled Network of Networks

We study diffusion and consensus dynamics in a Network of Networks model. In this model, there is a collection of sub-networks, connected to one another using a small number of links. We consider a setting where the links between networks have small weights, or are used less frequently than links within each sub-network. Using spectral perturbation theory, we analyze the diffusion rate and convergence rate of the investigated systems. Our analysis shows that the first order approximation of the diffusion and convergence rates is independent of the topologies of the individual graphs; the rates depend only on the number of nodes in each graph and the topology of the connecting edges. The second order analysis shows a relationship between the diffusion and convergence rates and the information centrality of the connecting nodes within each sub-network. We further highlight these theoretical results through numerical examples.

cs.SI↗

arXiv2019

Formalizing Event-Driven Behavior of Serverless Applications

We present new operational semantics for serverless computing that model the event-driven relationships between serverless functions, as well as their interaction with platforms services such as databases and object stores. These semantics precisely encapsulate how control transfers between functions, both directly and through reads and writes to platform services. We use these semantics to define the notion of the service call graph for serverless applications that captures program flows through functions and services. Finally, we construct service call graphs for twelve serverless JavaScript applications, using a prototype of our call graph construction algorithm, and we evaluate their accuracy.

cs.PL↗

arXiv2019

Submodularity in Systems with Higher Order Consensus with Absolute Information

We investigate the performance of m-th order consensus systems with stochastic external perturbations, where a subset of leader nodes incorporates absolute information into their control laws. The system performance is measured by its coherence, an $H_2$ norm that quantifies the total steady-state variance of the deviation from the desired trajectory. We first give conditions under which such systems are stable, and we derive expressions for coherence in stable second, third, and fourth order systems. We next study the problem of how to identify a set of leaders that optimizes coherence. To address this problem, we define set functions that quantify each system's coherence and prove that these functions are submodular. This allows the use of an efficient greedy algorithm that to find a leader set with which coherence is within a constant bound of optimal. We demonstrate the performance of the greedy algorithm empirically, and further, we show that the optimal leader sets for the different orders of consensus dynamics do not necessarily coincide.

math.OC↗

arXiv2019

Maximizing Diversity of Opinion in Social Networks

We study the problem of maximizing opinion diversity in a social network that includes opinion leaders with binary opposing opinions. The members of the network who are not leaders form their opinions using the French-DeGroot model of opinion dynamics. To quantify the diversity of such a system, we adapt two diversity measures from ecology to our setting, the Simpson Diversity Index and the Shannon Index. Using these two measures, we formalize the problem of how to place a single leader with opinion 1, given a network with a leader with opinion 0, so as to maximize the opinion diversity. We give analytical solutions to these problems for paths, cycles, and trees, and we highlight our results through a numerical example.

math.OC↗

arXiv2018

EdgeBench: Benchmarking Edge Computing Platforms

The emerging trend of edge computing has led several cloud providers to release their own platforms for performing computation at the 'edge' of the network. We compare two such platforms, Amazon AWS Greengrass and Microsoft Azure IoT Edge, using a new benchmark comprising a suite of performance metrics. We also compare the performance of the edge frameworks to cloud-only implementations available in their respective cloud ecosystems. Amazon AWS Greengrass and Azure IoT Edge use different underlying technologies, edge Lambda functions vs. containers, and so we also elaborate on platform features available to developers. Our study shows that both of these edge platforms provide comparable performance, which nevertheless differs in important ways for key types of workloads used in edge applications. Finally, we discuss several current issues and challenges we faced in deploying these platforms.

cs.NI↗

arXiv2018

BubbleTouch: A Quasi-Static Tactile Skin Simulator

We present BubbleTouch, an open source quasi-static simulator for robotic tactile skins. BubbleTouch can be used to simulate contact with a robot's tactile skin patches as it interacts with humans and objects. The simulator creates detailed traces of contact forces that can be used in experiments in tactile contact activities. We summarize the design of BubbleTouch and highlight our recent work that uses BubbleTouch for experiments with tactile object recognition.

cs.RO↗

arXiv2018

Maximizing the Number of Spanning Trees in a Connected Graph

We study the problem of maximizing the number of spanning trees in a connected graph by adding at most $k$ edges from a given candidate edge set. We give both algorithmic and hardness results for this problem: - We give a greedy algorithm that, using submodularity, obtains an approximation ratio of $(1 - 1/e - ε)$ in the exponent of the number of spanning trees for any $ε> 0$ in time $\tilde{O}(m ε^{-1} + (n + q) ε^{-3})$, where $m$ and $q$ is the number of edges in the original graph and the candidate edge set, respectively. Our running time is optimal with respect to the input size up to logarithmic factors, and substantially improves upon the $O(n^3)$ running time of the previous proposed greedy algorithm with approximation ratio $(1 - 1/e)$ in the exponent. Notably, the independence of our running time of $k$ is novel, comparing to conventional top-$k$ selections on graphs that usually run in $Ω(mk)$ time. A key ingredient of our greedy algorithm is a routine for maintaining effective resistances under edge additions in an online-offline hybrid setting. - We show the exponential inapproximability of this problem by proving that there exists a constant $c > 0$ such that it is NP-hard to approximate the optimum number of spanning trees in the exponent within $(1 - c)$. This inapproximability result follows from a reduction from the minimum path cover in undirected graphs, whose hardness again follows from the constant inapproximability of the Traveling Salesman Problem (TSP) with distances 1 and 2. Thus, the approximation ratio of our algorithm is also optimal up to a constant factor in the exponent. To our knowledge, this is the first hardness of approximation result for maximizing the number of spanning trees in a graph, or equivalently, by Kirchhoff's matrix-tree theorem, maximizing the determinant of an SDDM matrix.

cs.DS↗

arXiv2018

Scale-free Loopy Structure is Resistant to Noise in Consensus Dynamics in Complex Networks

The vast majority of real-world networks are scale-free, loopy, and sparse, with a power-law degree distribution and a constant average degree. In this paper, we study first-order consensus dynamics in binary scale-free networks, where vertices are subject to white noise. We focus on the coherence of networks characterized in terms of the $H_2$-norm, which quantifies how closely agents track the consensus value. We first provide a lower bound of coherence of a network in terms of its average degree, which is independent of the network order. We then study the coherence of some sparse, scale-free real-world networks, which approaches a constant. We also study numerically the coherence of Barabási-Albert networks and high-dimensional random Apollonian networks, which also converges to a constant when the networks grow. Finally, based on the connection of coherence and the Kirchhoff index, we study analytically the coherence of two deterministically-growing sparse networks and obtain the exact expressions, which tend to small constants. Our results indicate that the effect of noise on the consensus dynamics in power-law networks is negligible. We argue that scale-free topology, together with loopy structure, is responsible for the strong robustness with respect to noisy consensus dynamics in power-law networks.

eess.SY↗

arXiv2017

Submodular Optimization for Consensus Networks with Noise-Corrupted Leaders

We consider the leader selection problem in a network with consensus dynamics where both leader and follower agents are subject to stochastic external disturbances. The performance of the system is quantified by the total steady-state variance of the node states, and the goal is to identify the set of leaders that minimizes this variance. We first show that this performance measure can be expressed as a submodular set function over the nodes in the network. We then use this result to analyze the performance of two greedy, polynomial-time algorithms for leader selection, showing that the leader sets produced by the greedy algorithms are within provable bounds of optimal.

math.OC↗

arXiv2017

Biharmonic Distance and the Performance of Second-Order Consensus Networks with Stochastic Disturbances

We study second order consensus dynamics with random additive disturbances. We investigate three different performance measures: the steady-state variance of pairwise differences between vertex states, the steady-state variance of the deviation of each vertex state from the average, and the total steady-state variance of the system. We show that these performance measures are closely related to the biharmonic distance; the square of the biharmonic distance plays similar role in the system performance as resistance distances plays in the performance of first-order noisy consensus dynamics. We further define the new concepts of biharmonic Kirchhoff index and vertex centrality based on the biharmonic distance. Finally, we derive analytical results for the performance measures and concepts for complete graphs, star graphs, cycles, and paths, and we use this analysis to compare the asymptotic behavior of the steady-variance in first- and second-order systems.

math.OC↗