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Documents authored by Pawłowski, Michał

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APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2026.26
Online TCP Acknowledgment Under General Delays

Authors: Sujoy Bhore, Michał Pawłowski, and Seeun William Umboh

Published in: LIPIcs, Volume 392, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026)

Abstract
In a seminal work, Dooly, Goldman, and Scott (STOC 1998; JACM 2001) introduced the classic Online TCP Acknowledgment problem. In this problem, a sequence of n packets arrives over time, and the objective is to minimize both the number of acknowledgments sent and the total delay experienced by the packets. They showed that a natural greedy algorithm, which acknowledges when the delay of pending packets equals the acknowledgment cost, is 2-competitive. Online TCP Acknowledgment is the canonical online problem with delay, capturing the fundamental tradeoff between reducing service cost through batching and the delay incurred by pending requests. Prior work has largely focused on richer service-cost models, e.g., Joint Replenishment and Multi-Level Aggregation. However, other than the work of Albers and Bals (SODA 2003), which studies maximum delay and closely related objectives, not much is known about general delay costs beyond the sum of delay costs of requests. In this work, we study Online TCP Acknowledgment under two generalized delay-cost models that we call batch-aware and batch-oblivious. In the batch-aware model, each batch incurs a delay cost that depends on the packet delays within that batch. For the max-over-batches objective, which generalizes Albers and Bals, we show that greedy remains 2-competitive for every monotone batch-delay function. For the sum-over-batches objective, the picture changes sharply: greedy is Ω(n)-competitive, and the optimal deterministic competitive ratio is Θ(log n). Our matching upper bound requires only the minimal assumption that the batch delay function is monotone. In the batch-oblivious model, the delay cost is a function of the global packet-delay vector. We show that greedy is 2-competitive for continuous submodular delay costs, and more generally under a weaker zero-coordinate diminishing-marginals condition. This yields 2-competitive algorithms for 𝓁_p norms, Top-k norms, and ordered norms. Using the submodular-norm approximation of Patton, Russo, and Singla, we also obtain an O(log n)-competitive algorithm for arbitrary symmetric norms.
Cite as

Sujoy Bhore, Michał Pawłowski, and Seeun William Umboh. Online TCP Acknowledgment Under General Delays. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 392, pp. 26:1-26:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bhore_et_al:LIPIcs.APPROX/RANDOM.2026.26,
  author =	{Bhore, Sujoy and Paw{\l}owski, Micha{\l} and Umboh, Seeun William},
  title =	{{Online TCP Acknowledgment Under General Delays}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026)},
  pages =	{26:1--26:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-449-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{392},
  editor =	{Singh, Mohit and Gur, Tom},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2026.26},
  URN =		{urn:nbn:de:0030-drops-277435},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2026.26},
  annote =	{Keywords: Online Algorithms, TCP Acknowledgment, General Delay Functions}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2024.49
Online Multi-Level Aggregation with Delays and Stochastic Arrivals

Authors: Mathieu Mari, Michał Pawłowski, Runtian Ren, and Piotr Sankowski

Published in: LIPIcs, Volume 322, 35th International Symposium on Algorithms and Computation (ISAAC 2024)

Abstract
This paper presents a new research direction for online Multi-Level Aggregation (MLA) with delays. Given an edge-weighted rooted tree T as input, a sequence of requests arriving at its vertices needs to be served in an online manner. A request r is characterized by two parameters: its arrival time t(r) > 0 and location l(r) being a vertex in tree T. Once r arrives, we can either serve it immediately or postpone this action until any time t > t(r). A request that has not been served at its arrival time is called pending up to the moment it gets served. We can serve several pending requests at the same time, paying a service cost equal to the weight of the subtree containing the locations of all the requests served and the root of T. Postponing the service of a request r to time t > t(r) generates an additional delay cost of t - t(r). The goal is to serve all requests in an online manner such that the total cost (i.e., the total sum of service and delay costs) is minimized. The MLA problem is a generalization of several well-studied problems, including the TCP Acknowledgment (trees of depth 1), Joint Replenishment (depth 2), and Multi-Level Message Aggregation (arbitrary depth). The current best algorithm achieves a competitive ratio of O(d²), where d denotes the depth of the tree. Here, we consider a stochastic version of MLA where the requests follow a Poisson arrival process. We present a deterministic online algorithm that achieves a constant ratio of expectations, meaning that the ratio between the expected costs of the solution generated by our algorithm and the optimal offline solution is bounded by a constant. Our algorithm is obtained by carefully combining two strategies. In the first one, we plan periodic oblivious visits to the subset of frequent vertices, whereas, in the second one, we greedily serve the pending requests in the remaining vertices. This problem is complex enough to demonstrate a very rare phenomenon that "single-minded" or "sample-average" strategies are not enough in stochastic optimization.
Cite as

Mathieu Mari, Michał Pawłowski, Runtian Ren, and Piotr Sankowski. Online Multi-Level Aggregation with Delays and Stochastic Arrivals. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 49:1-49:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{mari_et_al:LIPIcs.ISAAC.2024.49,
  author =	{Mari, Mathieu and Paw{\l}owski, Micha{\l} and Ren, Runtian and Sankowski, Piotr},
  title =	{{Online Multi-Level Aggregation with Delays and Stochastic Arrivals}},
  booktitle =	{35th International Symposium on Algorithms and Computation (ISAAC 2024)},
  pages =	{49:1--49:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-354-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{322},
  editor =	{Mestre, Juli\'{a}n and Wirth, Anthony},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2024.49},
  URN =		{urn:nbn:de:0030-drops-221768},
  doi =		{10.4230/LIPIcs.ISAAC.2024.49},
  annote =	{Keywords: online algorithms, online network design, stochastic model, Poisson arrivals}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.12
Universal Optimization for Non-Clairvoyant Subadditive Joint Replenishment

Authors: Tomer Ezra, Stefano Leonardi, Michał Pawłowski, Matteo Russo, and Seeun William Umboh

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
The online joint replenishment problem (JRP) is a fundamental problem in the area of online problems with delay. Over the last decade, several works have studied generalizations of JRP with different cost functions for servicing requests. Most prior works on JRP and its generalizations have focused on the clairvoyant setting. Recently, Touitou [Noam Touitou, 2023] developed a non-clairvoyant framework that provided an O(√{n log n}) upper bound for a wide class of generalized JRP, where n is the number of request types. We advance the study of non-clairvoyant algorithms by providing a simpler, modular framework that matches the competitive ratio established by Touitou for the same class of generalized JRP. Our key insight is to leverage universal algorithms for Set Cover to approximate arbitrary monotone subadditive functions using a simple class of functions termed disjoint. This allows us to reduce the problem to several independent instances of the TCP Acknowledgement problem, for which a simple 2-competitive non-clairvoyant algorithm is known. The modularity of our framework is a major advantage as it allows us to tailor the reduction to specific problems and obtain better competitive ratios. In particular, we obtain tight O(√n)-competitive algorithms for two significant problems: Multi-Level Aggregation and Weighted Symmetric Subadditive Joint Replenishment. We also show that, in contrast, Touitou’s algorithm is Ω(√{n log n})-competitive for both of these problems.
Cite as

Tomer Ezra, Stefano Leonardi, Michał Pawłowski, Matteo Russo, and Seeun William Umboh. Universal Optimization for Non-Clairvoyant Subadditive Joint Replenishment. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 12:1-12:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ezra_et_al:LIPIcs.APPROX/RANDOM.2024.12,
  author =	{Ezra, Tomer and Leonardi, Stefano and Paw{\l}owski, Micha{\l} and Russo, Matteo and Umboh, Seeun William},
  title =	{{Universal Optimization for Non-Clairvoyant Subadditive Joint Replenishment}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{12:1--12:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.12},
  URN =		{urn:nbn:de:0030-drops-210050},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.12},
  annote =	{Keywords: Set Cover, Joint Replenishment, TCP-Acknowledgment, Subadditive Function Approximation, Multi-Level Aggregation}
}

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