The Multi-shop Ski Rental Problem

We consider the {\em multi-shop ski rental} problem. This problem generalizes the classic ski rental problem to a multi-shop setting, in which each shop has different prices for renting and purchasing a pair of skis, and a \emph{consumer} has to make decisions on when and where to buy. We are interested in the {\em optimal online (competitive-ratio minimizing) mixed strategy} from the consumer's perspective. For our problem in its basic form, we obtain exciting closed-form solutions and a linear time algorithm for computing them. We further demonstrate the generality of our approach by investigating three extensions of our basic problem, namely ones that consider costs incurred by entering a shop or switching to another shop. Our solutions to these problems suggest that the consumer must assign positive probability in \emph{exactly one} shop at any buying time. Our results apply to many real-world applications, ranging from cost management in \texttt{IaaS} cloud to scheduling in distributed computing

Online Replication Strategies for Distributed Data Stores

The rate at which data is produced at the network edge, e.g., collected from sensors and Internet of Things (IoT) devices, will soon exceed the storage and processing capabilities of a single system and the capacity of the network. Thus, data will need to be collected and preprocessed in distributed data stores - as part of a distributed database - at the network edge. Yet, even in this setup, the transfer of query results will incur prohibitive costs. To further reduce the data transfers, patterns in the workloads must be exploited. Particularly in IoT scenarios, we expect data access to be highly skewed. Most data will be store-only, while a fraction will be popular. Here, the replication of popular, raw data, as opposed to the shipment of partially redundant query results, can reduce the volume of data transfers over the network. In this paper, we design online strategies to decide between replicating data from data stores or forwarding the queries and retrieving their results. Our insight is that by profiling access patterns of the data we can lower the data transfer cost and the corresponding response times. We evaluate the benefit of our strategies using two real-world datasets

Online Algorithms with Uncertainty-Quantified Predictions

Online algorithms with predictions have become a trending topic in the field of beyond worst-case analysis of algorithms. These algorithms incorporate predictions about the future to obtain performance guarantees that are of high quality when the predictions are good, while still maintaining bounded worst-case guarantees when predictions are arbitrarily poor. In general, the algorithm is assumed to be unaware of the prediction's quality. However, recent developments in the machine learning literature have studied techniques for providing uncertainty quantification on machine-learned predictions, which describes how certain a model is about its quality. This paper examines the question of how to optimally utilize uncertainty-quantified predictions in the design of online algorithms. In particular, we consider predictions augmented with uncertainty quantification describing the likelihood of the ground truth falling in a certain range, designing online algorithms with these probabilistic predictions for two classic online problems: ski rental and online search. In each case, we demonstrate that non-trivial modifications to algorithm design are needed to fully leverage the probabilistic predictions. Moreover, we consider how to utilize more general forms of uncertainty quantification, proposing a framework based on online learning that learns to exploit uncertainty quantification to make optimal decisions in multi-instance settings

Fog-Driven Context-Aware Architecture for Node Discovery and Energy Saving Strategy for Internet of Things Environments

The consolidation of the Fog Computing paradigm and the ever-increasing diffusion of Internet of Things (IoT) and smart objects are paving the way toward new integrated solutions to efficiently provide services via short-mid range wireless connectivity. Being the most of the nodes mobile, the node discovery process assumes a crucial role for service seekers and providers, especially in IoT-fog environments where most of the devices run on battery. This paper proposes an original model and a fog-driven architecture for efficient node discovery in IoT environments. Our novel architecture exploits the location awareness provided by the fog paradigm to significantly reduce the power drain of the default baseline IoT discovery process. To this purpose, we propose a deterministic and competitive adaptive strategy to dynamically adjust our energy-saving techniques by deciding when to switch BLE interfaces ON/OFF based on the expected frequency of node approaching. Finally, the paper presents a thorough performance assessment that confirms the applicability of the proposed solution in several different applications scenarios. This evaluation aims also to highlight the impact of the nodes' dynamic arrival on discovery process performance

On Optimal Consistency-Robustness Trade-Off for Learning-Augmented Multi-Option Ski Rental

The learning-augmented multi-option ski rental problem generalizes the classical ski rental problem in two ways: the algorithm is provided with a prediction on the number of days we can ski, and the ski rental options now come with a variety of rental periods and prices to choose from, unlike the classical two-option setting. Subsequent to the initial study of the multi-option ski rental problem (without learning augmentation) due to Zhang, Poon, and Xu, significant progress has been made for this problem recently in particular. The problem is very well understood when we relinquish one of the two generalizations -- for the learning-augmented classical ski rental problem, algorithms giving best-possible trade-off between consistency and robustness exist; for the multi-option ski rental problem without learning augmentation, deterministic/randomized algorithms giving the best-possible competitiveness have been found. However, in presence of both generalizations, there remained a huge gap between the algorithmic and impossibility results. In fact, for randomized algorithms, we did not have any nontrivial lower bounds on the consistency-robustness trade-off before. This paper bridges this gap for both deterministic and randomized algorithms. For deterministic algorithms, we present a best-possible algorithm that completely matches the known lower bound. For randomized algorithms, we show the first nontrivial lower bound on the consistency-robustness trade-off, and also present an improved randomized algorithm. Our algorithm matches our lower bound on robustness within a factor of e/2 when the consistency is at most 1.086.Comment: 16 pages, 2 figure

Distributed Mega-Datasets: The Need for Novel Computing Primitives

© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.With the ongoing digitalization, an increasing number of sensors is becoming part of our digital infrastructure. These sensors produce highly, even globally, distributed data streams. The aggregate data rate of these streams far exceeds local storage and computing capabilities. Yet, for radical new services (e.g., predictive maintenance and autonomous driving), which depend on various control loops, this data needs to be analyzed in a timely fashion. In this position paper, we outline a system architecture that can effectively handle distributed mega-datasets using data aggregation. Hereby, we point out two research challenges: The need for (1) novel computing primitives that allow us to aggregate data at scale across multiple hierarchies (i.e., time and location) while answering a multitude of a priori unknown queries, and (2) transfer optimizations that enable rapid local and global decision making.EC/H2020/679158/EU/Resolving the Tussle in the Internet: Mapping, Architecture, and Policy Making/ResolutioNe