Dynamic Balanced Graph Partitioning

This paper initiates the study of the classic balanced graph partitioning problem from an online perspective: Given an arbitrary sequence of pairwise communication requests between $n$ nodes, with patterns that may change over time, the objective is to service these requests efficiently by partitioning the nodes into $\ell$ clusters, each of size $k$, such that frequently communicating nodes are located in the same cluster. The partitioning can be updated dynamically by migrating nodes between clusters. The goal is to devise online algorithms which jointly minimize the amount of inter-cluster communication and migration cost. The problem features interesting connections to other well-known online problems. For example, scenarios with $\ell=2$ generalize online paging, and scenarios with $k=2$ constitute a novel online variant of maximum matching. We present several lower bounds and algorithms for settings both with and without cluster-size augmentation. In particular, we prove that any deterministic online algorithm has a competitive ratio of at least $k$, even with significant augmentation. Our main algorithmic contributions are an $O(k \log{k})$-competitive deterministic algorithm for the general setting with constant augmentation, and a constant competitive algorithm for the maximum matching variant

Stitching IC Images

Image stitching software is used in many areas such as photogrammetry, biomedical imaging, and even amateur digital photography. However, these algorithms require relatively large image overlap, and for this reason they cannot be used to stitch the integrated circuit (IC) images, whose overlap is typically less than 60 pixels for a 4096 by 4096 pixel image. In this paper, we begin by using algorithmic graph theory to study optimal patterns for adding IC images one at a time to a grid. In the remaining sections we study ways of stitching all the images simultaneously using different optimisation approaches: least squares methods, simulated annealing, and nonlinear programming

A flexible receiver-driven cache replacement scheme for continuous media objects in best-effort networks

In this paper, we investigate the potential of caching to improve quality of reception (QoR) in the context of continuous media applications over best-effort networks. Specifically, we investigate the influence of parameters such as loss rate, jitter, delay and area in determining a proxy\u27s cache contents. We propose the use of a flexible cost function in caching algorithms and develop a framework for benchmarking continuous media caching algorithms. The cost function incorporates parameters in which, an administrator and or a client can tune to influence a proxy\u27s cache. Traditional caching systems typically base decisions around static schemes that do not take into account the interest of their receiver pool. Based on the flexible cost function, an improvised Greedy Dual (GD) algorithm called GD-multi has been developed for layered multiresolution multimedia streams. The effectiveness of the proposed scheme is evaluated by simulation-based performance studies. Performance of several caching schemes are evaluated and compared with those of the proposed scheme. Our empirical results indicate GD-multi performs well despite employing a generalized caching policy

Asymptotically-Optimal Incentive-Based En-Route Caching Scheme

Content caching at intermediate nodes is a very effective way to optimize the operations of Computer networks, so that future requests can be served without going back to the origin of the content. Several caching techniques have been proposed since the emergence of the concept, including techniques that require major changes to the Internet architecture such as Content Centric Networking. Few of these techniques consider providing caching incentives for the nodes or quality of service guarantees for content owners. In this work, we present a low complexity, distributed, and online algorithm for making caching decisions based on content popularity, while taking into account the aforementioned issues. Our algorithm performs en-route caching. Therefore, it can be integrated with the current TCP/IP model. In order to measure the performance of any online caching algorithm, we define the competitive ratio as the ratio of the performance of the online algorithm in terms of traffic savings to the performance of the optimal offline algorithm that has a complete knowledge of the future. We show that under our settings, no online algorithm can achieve a better competitive ratio than $\Omega(\log n)$, where $n$ is the number of nodes in the network. Furthermore, we show that under realistic scenarios, our algorithm has an asymptotically optimal competitive ratio in terms of the number of nodes in the network. We also study an extension to the basic algorithm and show its effectiveness through extensive simulations

Optimistic No-regret Algorithms for Discrete Caching

We take a systematic look at the problem of storing whole files in a cache with limited capacity in the context of optimistic learning, where the caching policy has access to a prediction oracle (provided by, e.g., a Neural Network). The successive file requests are assumed to be generated by an adversary, and no assumption is made on the accuracy of the oracle. In this setting, we provide a universal lower bound for prediction-assisted online caching and proceed to design a suite of policies with a range of performance-complexity trade-offs. All proposed policies offer sublinear regret bounds commensurate with the accuracy of the oracle. Our results substantially improve upon all recently-proposed online caching policies, which, being unable to exploit the oracle predictions, offer only $O(\sqrt{T})$ regret. In this pursuit, we design, to the best of our knowledge, the first comprehensive optimistic Follow-the-Perturbed leader policy, which generalizes beyond the caching problem. We also study the problem of caching files with different sizes and the bipartite network caching problem. Finally, we evaluate the efficacy of the proposed policies through extensive numerical experiments using real-world traces.Comment: Accepted to ACM SIGMETRICS 202

Online Caching with no Regret: Optimistic Learning via Recommendations

The design of effective online caching policies is an increasingly important problem for content distribution networks, online social networks and edge computing services, among other areas. This paper proposes a new algorithmic toolbox for tackling this problem through the lens of optimistic online learning. We build upon the Follow-the-Regularized-Leader (FTRL) framework, which is developed further here to include predictions for the file requests, and we design online caching algorithms for bipartite networks with fixed-size caches or elastic leased caches subject to time-average budget constraints. The predictions are provided by a content recommendation system that influences the users viewing activity and hence can naturally reduce the caching network's uncertainty about future requests. We also extend the framework to learn and utilize the best request predictor in cases where many are available. We prove that the proposed {optimistic} learning caching policies can achieve sub-zero performance loss (regret) for perfect predictions, and maintain the sub-linear regret bound $O(\sqrt T)$, which is the best achievable bound for policies that do not use predictions, even for arbitrary-bad predictions. The performance of the proposed algorithms is evaluated with detailed trace-driven numerical tests.Comment: arXiv admin note: substantial text overlap with arXiv:2202.1059