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Documents authored by Gotfryd, Karol

Document
DOI: 10.4230/LIPIcs.OPODIS.2024.29
On Reliability of the Extrema Propagation Technique in Random Environment

Authors: Jacek Cichoń, Dawid Dworzański, and Karol Gotfryd

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)

Abstract
We study the reliability of the following simple mechanism for spreading information in a communication network in the presence of random message loss. Initially, some nodes have information that they want to distribute throughout the network. Each node that has received the information tries to broadcast it to all its neighbors. However, due to interference or communication failures, each transmission between two nodes is broken independently with some fixed probability. This transmission mechanism is the basis for the extrema propagation technique, proposed and analyzed in [Carlos Baquero et al., 2012; Baquero et al., 2009; Jacek Cicho{ń} et al., 2012]. Extrema propagation is a simple but powerful method of spreading the extreme values stored by the nodes. In a fully reliable environment, only the number of rounds equal to the network diameter is required for all nodes to be informed. It was shown empirically in [Carlos Baquero et al., 2012] that it also performs well in the presence of link failures and message loss. Extrema propagation is an algorithmic framework that was adopted for designing efficient method for distributed data aggregation, such as estimation of cardinalities, sums, and averages, estimation of data distribution via histograms and random sampling (cf. [Baquero et al., 2009; Karol Gotfryd and Jacek Cichoń, 2023]). In this paper, we propose a formal network model in which random transmission failures occur and analyze the operation time of the extrema propagation technique for any connected network graph. We provide new general probabilistic upper bounds on the number of rounds needed to spread the extreme values that depend only on the number of nodes, the diameter of the network, and the probability of successful transmission. For some special families of graphs, we also derive specific, more accurate estimates. Our theoretical and experimental results confirm the reliability and efficiency of the extrema propagation technique in faulty or noisy environments.
Cite as

Jacek Cichoń, Dawid Dworzański, and Karol Gotfryd. On Reliability of the Extrema Propagation Technique in Random Environment. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{cichon_et_al:LIPIcs.OPODIS.2024.29,
  author =	{Cicho\'{n}, Jacek and Dworza\'{n}ski, Dawid and Gotfryd, Karol},
  title =	{{On Reliability of the Extrema Propagation Technique in Random Environment}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{29:1--29:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.29},
  URN =		{urn:nbn:de:0030-drops-225657},
  doi =		{10.4230/LIPIcs.OPODIS.2024.29},
  annote =	{Keywords: wireless ad-hoc networks, extrema propagation, distributed data aggregation, fault tolerant aggregation, randomly evolving networks}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.22
Tree Exploration in Dual-Memory Model

Authors: Dominik Bojko, Karol Gotfryd, Dariusz R. Kowalski, and Dominik Pająk

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
We study the problem of online tree exploration by a deterministic mobile agent. Our main objective is to establish what features of the model of the mobile agent and the environment allow linear exploration time. We study agents that, upon entering a node, do not receive as input the edge via which they entered. In such model, deterministic memoryless exploration is infeasible, hence the agent needs to be allowed to use some memory. The memory can be located at the agent or at each node. The existing lower bounds show that if the memory is either only at the agent or only at the nodes, then the exploration needs superlinear time. We show that tree exploration in dual-memory model, with constant memory at the agent and logarithmic in the degree at each node is possible in linear time when one of the two additional features is present: fixed initial state of the memory at each node (so called clean memory) or a single movable token. We present two algorithms working in linear time for arbitrary trees in these two models. On the other hand, in our lower bound we show that if the agent has a single bit of memory and one bit is present at each node, then the exploration may require quadratic time even on paths, if the initial memory at nodes could be set arbitrarily (so called dirty memory). This shows that having clean node memory or a token allows linear time exploration of trees in the dual-memory model, but having neither of those features may lead to quadratic exploration time even on a simple path.
Cite as

Dominik Bojko, Karol Gotfryd, Dariusz R. Kowalski, and Dominik Pająk. Tree Exploration in Dual-Memory Model. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 22:1-22:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bojko_et_al:LIPIcs.MFCS.2022.22,
  author =	{Bojko, Dominik and Gotfryd, Karol and Kowalski, Dariusz R. and Paj\k{a}k, Dominik},
  title =	{{Tree Exploration in Dual-Memory Model}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{22:1--22:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.22},
  URN =		{urn:nbn:de:0030-drops-168207},
  doi =		{10.4230/LIPIcs.MFCS.2022.22},
  annote =	{Keywords: Graph exploration, agent, memory, tree, deterministic algorithms, lower bound}
}
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