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**Published in:** LIPIcs, Volume 209, 35th International Symposium on Distributed Computing (DISC 2021)

We consider the fundamental problems of size discovery and topology recognition in radio networks modeled by simple undirected connected graphs. Size discovery calls for all nodes to output the number of nodes in the graph, called its size, and in the task of topology recognition each node has to learn the topology of the graph and its position in it.
We do not assume collision detection: in case of a collision, node v does not hear anything (except the background noise that it also hears when no neighbor transmits). The time of a deterministic algorithm for each of the above problems is the worst-case number of rounds it takes to solve it. Nodes have labels which are (not necessarily different) binary strings. Each node knows its own label and can use it when executing the algorithm. The length of a labeling scheme is the largest length of a label.
For size discovery, we construct a labeling scheme of length O(log logΔ) (which is known to be optimal, even if collision detection is available) and we design an algorithm for this problem using this scheme and working in time O(log² n), where n is the size of the graph. We also show that time complexity O(log² n) is optimal for the problem of size discovery, whenever the labeling scheme is of optimal length O(log logΔ). For topology recognition, we construct a labeling scheme of length O(logΔ), and we design an algorithm for this problem using this scheme and working in time O (DΔ+min(Δ²,n)), where D is the diameter of the graph. We also show that the length of our labeling scheme is asymptotically optimal.

Adam Gańczorz, Tomasz Jurdziński, Mateusz Lewko, and Andrzej Pelc. Deterministic Size Discovery and Topology Recognition in Radio Networks with Short Labels. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{ganczorz_et_al:LIPIcs.DISC.2021.22, author = {Ga\'{n}czorz, Adam and Jurdzi\'{n}ski, Tomasz and Lewko, Mateusz and Pelc, Andrzej}, title = {{Deterministic Size Discovery and Topology Recognition in Radio Networks with Short Labels}}, booktitle = {35th International Symposium on Distributed Computing (DISC 2021)}, pages = {22:1--22:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-210-5}, ISSN = {1868-8969}, year = {2021}, volume = {209}, editor = {Gilbert, Seth}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2021.22}, URN = {urn:nbn:de:0030-drops-148242}, doi = {10.4230/LIPIcs.DISC.2021.22}, annote = {Keywords: size discovery, topology recognition, radio network, labeling scheme} }

Document

**Published in:** LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)

In this work we study stability of local memoryless packet scheduling policies in a distributed system of n nodes/queues under contention. The local policies at nodes may only access their current local queues, and have no other feedback from the underlying distributed system. Moreover, their memory is limited to some basic parameters. The packets arrive at queues according to arrival patterns controlled by an adversary restricted only by injection rate rho and burstiness b, or driven by a stochastic process; the former model analyzes worst-case stability while the latter - average case. We assume that the underlying distributed system is a classic shared channel, in which no two packets could be successfully scheduled (and removed from queues) at the same time. We show that there is a local memoryless scheduling policy which is both adversarially and stochastically stable for injection rates Omega(1/log n). Another algorithm achieves even higher - constant - stable injection rate, but only for a bounded range of burstiness. The first algorithm is utilizing properties of interleaved ultra-selectors, for which we prove stronger properties than known so far, while the second one is based on entirely new concept of selector with thresholds, unlike previously considered binary selectors/codes in the literature.
Note that popular Backoff algorithms, some of which achieve stability for constant (stochastic) injection rates [Johan Håstad et al., 1996], use memory to record current state (e.g., the number of unsuccessful transmissions or the result of random sampling in each window) as well as randomization and feedback from the channel; unlike solutions in this work, which are memoryless and do not rely on randomization or channel feedback (thus, could be used independently from the link layer protocols). {}

Paweł Garncarek, Tomasz Jurdziński, and Dariusz R. Kowalski. Stable Memoryless Queuing under Contention. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{garncarek_et_al:LIPIcs.DISC.2019.17, author = {Garncarek, Pawe{\l} and Jurdzi\'{n}ski, Tomasz and Kowalski, Dariusz R.}, title = {{Stable Memoryless Queuing under Contention}}, booktitle = {33rd International Symposium on Distributed Computing (DISC 2019)}, pages = {17:1--17:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-126-9}, ISSN = {1868-8969}, year = {2019}, volume = {146}, editor = {Suomela, Jukka}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.17}, URN = {urn:nbn:de:0030-drops-113244}, doi = {10.4230/LIPIcs.DISC.2019.17}, annote = {Keywords: packet scheduling, online algorithms, adversarial injections, stochastic injections, stability, memoryless algorithms} }

Document

**Published in:** LIPIcs, Volume 121, 32nd International Symposium on Distributed Computing (DISC 2018)

We study stability of local packet scheduling policies in a distributed system of n nodes. The local policies at nodes may only access their local queues, and have no other feedback from the underlying distributed system. The packets arrive at queues according to arrival patterns controlled by an adversary restricted only by injection rate rho and burstiness b. In this work, we assume that the underlying distributed system is a shared channel, in which in order to get rid of a packet from the queue, a node needs to schedule it for transmission on the channel and no other packet is scheduled for transmission at the same time. We show that there is a local adaptive scheduling policy with relatively small memory, which is universally stable on a shared channel, that is, it has bounded queues for any rho<1 and b >= 0. On the other hand, without memory the maximal stable injection rate is O(1/log n). We show a local memoryless (non-adaptive) scheduling policy based on novel idea of ultra strong selectors which is stable for slightly smaller injection c/log^2 n, for some constant c>0.

Pawel Garncarek, Tomasz Jurdzinski, and Dariusz R. Kowalski. Local Queuing Under Contention. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 28:1-28:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{garncarek_et_al:LIPIcs.DISC.2018.28, author = {Garncarek, Pawel and Jurdzinski, Tomasz and Kowalski, Dariusz R.}, title = {{Local Queuing Under Contention}}, booktitle = {32nd International Symposium on Distributed Computing (DISC 2018)}, pages = {28:1--28:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-092-7}, ISSN = {1868-8969}, year = {2018}, volume = {121}, editor = {Schmid, Ulrich and Widder, Josef}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.28}, URN = {urn:nbn:de:0030-drops-98172}, doi = {10.4230/LIPIcs.DISC.2018.28}, annote = {Keywords: Distributed algorithms, local queuing, shared channel, multiple-access channel, adversarial packet arrivals, stability, deterministic algorithms} }

Document

Brief Announcement

**Published in:** LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)

Recently, very fast deterministic and randomized algorithms have been obtained for connectivity and minimum spanning tree in the unicast congested clique. In contrast, no solution faster than a simple parallel implementation of the Boruvka's algorithm has been known for both problems in the broadcast congested clique. In this announcement, we present the first sub-logarithmic deterministic algorithm for connected components in the broadcast congested clique.

Tomasz Jurdzínski and Krzysztof Nowicki. Brief Announcement: On Connectivity in the Broadcast Congested Clique. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 54:1-54:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{jurdzinski_et_al:LIPIcs.DISC.2017.54, author = {Jurdz{\'\i}nski, Tomasz and Nowicki, Krzysztof}, title = {{Brief Announcement: On Connectivity in the Broadcast Congested Clique}}, booktitle = {31st International Symposium on Distributed Computing (DISC 2017)}, pages = {54:1--54:4}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-053-8}, ISSN = {1868-8969}, year = {2017}, volume = {91}, editor = {Richa, Andr\'{e}a}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.54}, URN = {urn:nbn:de:0030-drops-79903}, doi = {10.4230/LIPIcs.DISC.2017.54}, annote = {Keywords: congested clique, broadcast, connected components, bandwidth} }

Document

**Published in:** LIPIcs, Volume 209, 35th International Symposium on Distributed Computing (DISC 2021)

We consider the fundamental problems of size discovery and topology recognition in radio networks modeled by simple undirected connected graphs. Size discovery calls for all nodes to output the number of nodes in the graph, called its size, and in the task of topology recognition each node has to learn the topology of the graph and its position in it.
We do not assume collision detection: in case of a collision, node v does not hear anything (except the background noise that it also hears when no neighbor transmits). The time of a deterministic algorithm for each of the above problems is the worst-case number of rounds it takes to solve it. Nodes have labels which are (not necessarily different) binary strings. Each node knows its own label and can use it when executing the algorithm. The length of a labeling scheme is the largest length of a label.
For size discovery, we construct a labeling scheme of length O(log logΔ) (which is known to be optimal, even if collision detection is available) and we design an algorithm for this problem using this scheme and working in time O(log² n), where n is the size of the graph. We also show that time complexity O(log² n) is optimal for the problem of size discovery, whenever the labeling scheme is of optimal length O(log logΔ). For topology recognition, we construct a labeling scheme of length O(logΔ), and we design an algorithm for this problem using this scheme and working in time O (DΔ+min(Δ²,n)), where D is the diameter of the graph. We also show that the length of our labeling scheme is asymptotically optimal.

Adam Gańczorz, Tomasz Jurdziński, Mateusz Lewko, and Andrzej Pelc. Deterministic Size Discovery and Topology Recognition in Radio Networks with Short Labels. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{ganczorz_et_al:LIPIcs.DISC.2021.22, author = {Ga\'{n}czorz, Adam and Jurdzi\'{n}ski, Tomasz and Lewko, Mateusz and Pelc, Andrzej}, title = {{Deterministic Size Discovery and Topology Recognition in Radio Networks with Short Labels}}, booktitle = {35th International Symposium on Distributed Computing (DISC 2021)}, pages = {22:1--22:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-210-5}, ISSN = {1868-8969}, year = {2021}, volume = {209}, editor = {Gilbert, Seth}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2021.22}, URN = {urn:nbn:de:0030-drops-148242}, doi = {10.4230/LIPIcs.DISC.2021.22}, annote = {Keywords: size discovery, topology recognition, radio network, labeling scheme} }

Document

**Published in:** LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)

In this work we study stability of local memoryless packet scheduling policies in a distributed system of n nodes/queues under contention. The local policies at nodes may only access their current local queues, and have no other feedback from the underlying distributed system. Moreover, their memory is limited to some basic parameters. The packets arrive at queues according to arrival patterns controlled by an adversary restricted only by injection rate rho and burstiness b, or driven by a stochastic process; the former model analyzes worst-case stability while the latter - average case. We assume that the underlying distributed system is a classic shared channel, in which no two packets could be successfully scheduled (and removed from queues) at the same time. We show that there is a local memoryless scheduling policy which is both adversarially and stochastically stable for injection rates Omega(1/log n). Another algorithm achieves even higher - constant - stable injection rate, but only for a bounded range of burstiness. The first algorithm is utilizing properties of interleaved ultra-selectors, for which we prove stronger properties than known so far, while the second one is based on entirely new concept of selector with thresholds, unlike previously considered binary selectors/codes in the literature.
Note that popular Backoff algorithms, some of which achieve stability for constant (stochastic) injection rates [Johan Håstad et al., 1996], use memory to record current state (e.g., the number of unsuccessful transmissions or the result of random sampling in each window) as well as randomization and feedback from the channel; unlike solutions in this work, which are memoryless and do not rely on randomization or channel feedback (thus, could be used independently from the link layer protocols). {}

Paweł Garncarek, Tomasz Jurdziński, and Dariusz R. Kowalski. Stable Memoryless Queuing under Contention. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{garncarek_et_al:LIPIcs.DISC.2019.17, author = {Garncarek, Pawe{\l} and Jurdzi\'{n}ski, Tomasz and Kowalski, Dariusz R.}, title = {{Stable Memoryless Queuing under Contention}}, booktitle = {33rd International Symposium on Distributed Computing (DISC 2019)}, pages = {17:1--17:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-126-9}, ISSN = {1868-8969}, year = {2019}, volume = {146}, editor = {Suomela, Jukka}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.17}, URN = {urn:nbn:de:0030-drops-113244}, doi = {10.4230/LIPIcs.DISC.2019.17}, annote = {Keywords: packet scheduling, online algorithms, adversarial injections, stochastic injections, stability, memoryless algorithms} }

Document

**Published in:** LIPIcs, Volume 121, 32nd International Symposium on Distributed Computing (DISC 2018)

We study stability of local packet scheduling policies in a distributed system of n nodes. The local policies at nodes may only access their local queues, and have no other feedback from the underlying distributed system. The packets arrive at queues according to arrival patterns controlled by an adversary restricted only by injection rate rho and burstiness b. In this work, we assume that the underlying distributed system is a shared channel, in which in order to get rid of a packet from the queue, a node needs to schedule it for transmission on the channel and no other packet is scheduled for transmission at the same time. We show that there is a local adaptive scheduling policy with relatively small memory, which is universally stable on a shared channel, that is, it has bounded queues for any rho<1 and b >= 0. On the other hand, without memory the maximal stable injection rate is O(1/log n). We show a local memoryless (non-adaptive) scheduling policy based on novel idea of ultra strong selectors which is stable for slightly smaller injection c/log^2 n, for some constant c>0.

Pawel Garncarek, Tomasz Jurdzinski, and Dariusz R. Kowalski. Local Queuing Under Contention. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 28:1-28:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{garncarek_et_al:LIPIcs.DISC.2018.28, author = {Garncarek, Pawel and Jurdzinski, Tomasz and Kowalski, Dariusz R.}, title = {{Local Queuing Under Contention}}, booktitle = {32nd International Symposium on Distributed Computing (DISC 2018)}, pages = {28:1--28:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-092-7}, ISSN = {1868-8969}, year = {2018}, volume = {121}, editor = {Schmid, Ulrich and Widder, Josef}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.28}, URN = {urn:nbn:de:0030-drops-98172}, doi = {10.4230/LIPIcs.DISC.2018.28}, annote = {Keywords: Distributed algorithms, local queuing, shared channel, multiple-access channel, adversarial packet arrivals, stability, deterministic algorithms} }

Document

Brief Announcement

**Published in:** LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)

Recently, very fast deterministic and randomized algorithms have been obtained for connectivity and minimum spanning tree in the unicast congested clique. In contrast, no solution faster than a simple parallel implementation of the Boruvka's algorithm has been known for both problems in the broadcast congested clique. In this announcement, we present the first sub-logarithmic deterministic algorithm for connected components in the broadcast congested clique.

Tomasz Jurdzínski and Krzysztof Nowicki. Brief Announcement: On Connectivity in the Broadcast Congested Clique. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 54:1-54:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{jurdzinski_et_al:LIPIcs.DISC.2017.54, author = {Jurdz{\'\i}nski, Tomasz and Nowicki, Krzysztof}, title = {{Brief Announcement: On Connectivity in the Broadcast Congested Clique}}, booktitle = {31st International Symposium on Distributed Computing (DISC 2017)}, pages = {54:1--54:4}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-053-8}, ISSN = {1868-8969}, year = {2017}, volume = {91}, editor = {Richa, Andr\'{e}a}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.54}, URN = {urn:nbn:de:0030-drops-79903}, doi = {10.4230/LIPIcs.DISC.2017.54}, annote = {Keywords: congested clique, broadcast, connected components, bandwidth} }

Document

**Published in:** LIPIcs, Volume 209, 35th International Symposium on Distributed Computing (DISC 2021)

We consider the fundamental problems of size discovery and topology recognition in radio networks modeled by simple undirected connected graphs. Size discovery calls for all nodes to output the number of nodes in the graph, called its size, and in the task of topology recognition each node has to learn the topology of the graph and its position in it.
We do not assume collision detection: in case of a collision, node v does not hear anything (except the background noise that it also hears when no neighbor transmits). The time of a deterministic algorithm for each of the above problems is the worst-case number of rounds it takes to solve it. Nodes have labels which are (not necessarily different) binary strings. Each node knows its own label and can use it when executing the algorithm. The length of a labeling scheme is the largest length of a label.
For size discovery, we construct a labeling scheme of length O(log logΔ) (which is known to be optimal, even if collision detection is available) and we design an algorithm for this problem using this scheme and working in time O(log² n), where n is the size of the graph. We also show that time complexity O(log² n) is optimal for the problem of size discovery, whenever the labeling scheme is of optimal length O(log logΔ). For topology recognition, we construct a labeling scheme of length O(logΔ), and we design an algorithm for this problem using this scheme and working in time O (DΔ+min(Δ²,n)), where D is the diameter of the graph. We also show that the length of our labeling scheme is asymptotically optimal.

Adam Gańczorz, Tomasz Jurdziński, Mateusz Lewko, and Andrzej Pelc. Deterministic Size Discovery and Topology Recognition in Radio Networks with Short Labels. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{ganczorz_et_al:LIPIcs.DISC.2021.22, author = {Ga\'{n}czorz, Adam and Jurdzi\'{n}ski, Tomasz and Lewko, Mateusz and Pelc, Andrzej}, title = {{Deterministic Size Discovery and Topology Recognition in Radio Networks with Short Labels}}, booktitle = {35th International Symposium on Distributed Computing (DISC 2021)}, pages = {22:1--22:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-210-5}, ISSN = {1868-8969}, year = {2021}, volume = {209}, editor = {Gilbert, Seth}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2021.22}, URN = {urn:nbn:de:0030-drops-148242}, doi = {10.4230/LIPIcs.DISC.2021.22}, annote = {Keywords: size discovery, topology recognition, radio network, labeling scheme} }

Document

**Published in:** LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)

In this work we study stability of local memoryless packet scheduling policies in a distributed system of n nodes/queues under contention. The local policies at nodes may only access their current local queues, and have no other feedback from the underlying distributed system. Moreover, their memory is limited to some basic parameters. The packets arrive at queues according to arrival patterns controlled by an adversary restricted only by injection rate rho and burstiness b, or driven by a stochastic process; the former model analyzes worst-case stability while the latter - average case. We assume that the underlying distributed system is a classic shared channel, in which no two packets could be successfully scheduled (and removed from queues) at the same time. We show that there is a local memoryless scheduling policy which is both adversarially and stochastically stable for injection rates Omega(1/log n). Another algorithm achieves even higher - constant - stable injection rate, but only for a bounded range of burstiness. The first algorithm is utilizing properties of interleaved ultra-selectors, for which we prove stronger properties than known so far, while the second one is based on entirely new concept of selector with thresholds, unlike previously considered binary selectors/codes in the literature.
Note that popular Backoff algorithms, some of which achieve stability for constant (stochastic) injection rates [Johan Håstad et al., 1996], use memory to record current state (e.g., the number of unsuccessful transmissions or the result of random sampling in each window) as well as randomization and feedback from the channel; unlike solutions in this work, which are memoryless and do not rely on randomization or channel feedback (thus, could be used independently from the link layer protocols). {}

Paweł Garncarek, Tomasz Jurdziński, and Dariusz R. Kowalski. Stable Memoryless Queuing under Contention. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{garncarek_et_al:LIPIcs.DISC.2019.17, author = {Garncarek, Pawe{\l} and Jurdzi\'{n}ski, Tomasz and Kowalski, Dariusz R.}, title = {{Stable Memoryless Queuing under Contention}}, booktitle = {33rd International Symposium on Distributed Computing (DISC 2019)}, pages = {17:1--17:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-126-9}, ISSN = {1868-8969}, year = {2019}, volume = {146}, editor = {Suomela, Jukka}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.17}, URN = {urn:nbn:de:0030-drops-113244}, doi = {10.4230/LIPIcs.DISC.2019.17}, annote = {Keywords: packet scheduling, online algorithms, adversarial injections, stochastic injections, stability, memoryless algorithms} }

Document

**Published in:** LIPIcs, Volume 121, 32nd International Symposium on Distributed Computing (DISC 2018)

We study stability of local packet scheduling policies in a distributed system of n nodes. The local policies at nodes may only access their local queues, and have no other feedback from the underlying distributed system. The packets arrive at queues according to arrival patterns controlled by an adversary restricted only by injection rate rho and burstiness b. In this work, we assume that the underlying distributed system is a shared channel, in which in order to get rid of a packet from the queue, a node needs to schedule it for transmission on the channel and no other packet is scheduled for transmission at the same time. We show that there is a local adaptive scheduling policy with relatively small memory, which is universally stable on a shared channel, that is, it has bounded queues for any rho<1 and b >= 0. On the other hand, without memory the maximal stable injection rate is O(1/log n). We show a local memoryless (non-adaptive) scheduling policy based on novel idea of ultra strong selectors which is stable for slightly smaller injection c/log^2 n, for some constant c>0.

Pawel Garncarek, Tomasz Jurdzinski, and Dariusz R. Kowalski. Local Queuing Under Contention. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 28:1-28:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{garncarek_et_al:LIPIcs.DISC.2018.28, author = {Garncarek, Pawel and Jurdzinski, Tomasz and Kowalski, Dariusz R.}, title = {{Local Queuing Under Contention}}, booktitle = {32nd International Symposium on Distributed Computing (DISC 2018)}, pages = {28:1--28:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-092-7}, ISSN = {1868-8969}, year = {2018}, volume = {121}, editor = {Schmid, Ulrich and Widder, Josef}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.28}, URN = {urn:nbn:de:0030-drops-98172}, doi = {10.4230/LIPIcs.DISC.2018.28}, annote = {Keywords: Distributed algorithms, local queuing, shared channel, multiple-access channel, adversarial packet arrivals, stability, deterministic algorithms} }

Document

Brief Announcement

**Published in:** LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)

Recently, very fast deterministic and randomized algorithms have been obtained for connectivity and minimum spanning tree in the unicast congested clique. In contrast, no solution faster than a simple parallel implementation of the Boruvka's algorithm has been known for both problems in the broadcast congested clique. In this announcement, we present the first sub-logarithmic deterministic algorithm for connected components in the broadcast congested clique.

Tomasz Jurdzínski and Krzysztof Nowicki. Brief Announcement: On Connectivity in the Broadcast Congested Clique. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 54:1-54:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{jurdzinski_et_al:LIPIcs.DISC.2017.54, author = {Jurdz{\'\i}nski, Tomasz and Nowicki, Krzysztof}, title = {{Brief Announcement: On Connectivity in the Broadcast Congested Clique}}, booktitle = {31st International Symposium on Distributed Computing (DISC 2017)}, pages = {54:1--54:4}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-053-8}, ISSN = {1868-8969}, year = {2017}, volume = {91}, editor = {Richa, Andr\'{e}a}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.54}, URN = {urn:nbn:de:0030-drops-79903}, doi = {10.4230/LIPIcs.DISC.2017.54}, annote = {Keywords: congested clique, broadcast, connected components, bandwidth} }

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