Maciej Pacut

Yuval Emek, Yuval Gil, Maciej Pacut et al.

We introduce a novel method for the rigorous quantitative evaluation of online algorithms that relaxes the "radical worst-case" perspective of classic competitive analysis. In contrast to prior work, our method, referred to as randomly infused advice (RIA), does not make any probabilistic assumptions about the input sequence and does not rely on the development of designated online algorithms. Rather, it can be applied to existing online randomized algorithms, introducing a means to evaluate their performance in scenarios that lie outside the radical worst-case regime. More concretely, an online algorithm ALG with RIA benefits from pieces of advice generated by an omniscient but not entirely reliable oracle. The crux of the new method is that the advice is provided to ALG by writing it into the buffer B from which ALG normally reads its random bits, hence allowing us to augment it through a very simple and non-intrusive interface. The (un)reliability of the oracle is captured via a parameter 0 {\le} α {\le} 1 that determines the probability (per round) that the advice is successfully infused by the oracle; if the advice is not infused, which occurs with probability 1 - α, then the buffer B contains fresh random bits (as in the classic online setting). The applicability of the new RIA method is demonstrated by applying it to three extensively studied online problems: paging, uniform metrical task systems, and online set cover. For these problems, we establish new upper bounds on the competitive ratio of classic online algorithms that improve as the infusion parameter α increases. These are complemented with (often tight) lower bounds on the competitive ratio of online algorithms with RIA for the three problems.

Julien Dallot, Yuval Emek, Yuval Gil et al.

This paper introduces a new model for ML-augmented online decision making, called online algorithms with unreliable guidance (OAG). This model completely separates between the predictive and algorithmic components, thus offering a single well-defined analysis framework that relies solely on the considered problem. Formulated through the lens of request-answer games, an OAG algorithm receives, with each incoming request, a piece of guidance which is taken from the problem's answer space; ideally, this guidance is the optimal answer for the current request, however with probability $β$, the guidance is adversarially corrupted. The goal is to develop OAG algorithms that admit good competitiveness when $β= 0$ (a.k.a. consistency) as well as when $β= 1$ (a.k.a. robustness); the appealing notion of smoothness, that in most prior work required a dedicated loss function, now arises naturally as $β$ shifts from $0$ to $1$. We then describe a systematic method, called the drop or trust blindly (DTB) compiler, which transforms any online algorithm into a learning-augmented online algorithm in the OAG model. Given a prediction-oblivious online algorithm, its learning-augmented counterpart produced by applying the DTB compiler either follows the incoming guidance blindly or ignores it altogether and proceeds as the initial algorithm would have; the choice between these two alternatives is based on the outcome of a (biased) coin toss. As our main technical contribution, we prove (rigorously) that although remarkably simple, the class of algorithms produced via the DTB compiler includes algorithms with attractive consistency-robustness guarantees for three classic online problems: for caching and uniform metrical task systems our algorithms are optimal, whereas for bipartite matching (with adversarial arrival order), our algorithm outperforms the state-of-the-art.

Julien Dallot, Darya Melnyk, Maciej Pacut et al.

Graph embedding is a fundamental problem of mapping nodes of a guest graph into a host graph while minimizing the distance distortion, with broad applications, including virtual network embeddings into physical topologies, VLSI design, or community detection in social networks. However, in many real-world applications the guest graph changes over time and the embedding can adapt to these changes (e.g. virtual machine migration in network embeddings). Static embeddings are inherently inefficient in comparison to adaptive embeddings, but it remains an unresolved algorithmic challenge to design efficient embedding algorithms that adapt to the demand on-the-fly, i.e., that are online. In this paper, we derive optimal deterministic and randomized online algorithms for the online graph embedding problem in star host graphs. This is an essential building block on the way to design algorithms for more complex host graphs, representing a single node and its neighborhood. We start by presenting a $1.5$-competitive deterministic algorithm and showing that no deterministic algorithm can perform better. Our main contribution is a randomized algorithm that achieves a significantly better competitive ratio of $11/9 \approx 1.222$. Both the deterministic and the randomized algorithms are optimal, which we prove by deriving tight lower bounds for the competitiveness of any algorithm.

Vamsi Addanki, Maciej Pacut, Stefan Schmid

Packet buffers in datacenter switches are shared across all the switch ports in order to improve the overall throughput. The trend of shrinking buffer sizes in datacenter switches makes buffer sharing extremely challenging and a critical performance issue. Literature suggests that push-out buffer sharing algorithms have significantly better performance guarantees compared to drop-tail algorithms. Unfortunately, switches are unable to benefit from these algorithms due to lack of support for push-out operations in hardware. Our key observation is that drop-tail buffers can emulate push-out buffers if the future packet arrivals are known ahead of time. This suggests that augmenting drop-tail algorithms with predictions about the future arrivals has the potential to significantly improve performance. This paper is the first research attempt in this direction. We propose Credence, a drop-tail buffer sharing algorithm augmented with machine-learned predictions. Credence can unlock the performance only attainable by push-out algorithms so far. Its performance hinges on the accuracy of predictions. Specifically, Credence achieves near-optimal performance of the best known push-out algorithm LQD (Longest Queue Drop) with perfect predictions, but gracefully degrades to the performance of the simplest drop-tail algorithm Complete Sharing when the prediction error gets arbitrarily worse. Our evaluations show that Credence improves throughput by $1.5$x compared to traditional approaches. In terms of flow completion times, we show that Credence improves upon the state-of-the-art approaches by up to $95\%$ using off-the-shelf machine learning techniques that are also practical in today's hardware. We believe this work opens several interesting future work opportunities both in systems and theory that we discuss at the end of this paper.

Marcin Bienkowski, Julien Dallot, Dominik Danelski et al.

Payment channel networks (PCNs) are a promising solution to make cryptocurrency transactions faster and more scalable. At their core, PCNs bypass the blockchain by routing the transactions through intermediary channels. However, a channel can forward a transaction only if it possesses the necessary funds: the problem of keeping the channels balanced is a current bottleneck on the PCN's transaction throughput. This paper considers the problem of maximizing the number of accepted transactions by a channel in a PCN. Previous works either considered the associated optimization problem with all transactions known in advance or developed heuristics tested on particular transaction datasets. This work however considers the problem in its purely online form where the transactions are arbitrary and revealed one after the other. We show that the problem can be modeled as a new online knapsack variant where the items (transaction proposals) can be either positive or negative depending on the direction of the transaction. The main contribution of this paper is a deterministic online algorithm that is $O(\log B)$-competitive, where $B$ is the knapsack capacity (initially allocated funds). We complement this result with an asymptotically matching lower bound of $Ω(\log B)$ which holds for any randomized algorithm, demonstrating our algorithm's optimality.

Michał Karpiński, Maciej Pacut

The goal of this paper is to propose and test a new memetic algorithm for the capacitated vehicle routing problem in parallel computing environment. In this paper we consider simple variation of vehicle routing problem in which the only parameter is the capacity of the vehicle and each client only needs one package. We present simple reduction to prove the existence of polynomial-time algorithm for capacity 2. We analyze the efficiency of the algorithm using hierarchical Parallel Random Access Machine (PRAM) model and run experiments with code written in CUDA (for capacities larger than 2).