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**Published in:** LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)

This paper initiates the study of the MAX-CUT problem in fully dynamic graphs. Given a graph G = (V,E), we present deterministic fully dynamic distributed and sequential algorithms to maintain a cut on G which always contains at least |E|/2 edges in sublinear update time under edge insertions and deletions to G. Our results include the following deterministic algorithms: i) an O(Δ) worst-case update time sequential algorithm, where Δ denotes the maximum degree of G, ii) the first fully dynamic distributed algorithm taking O(1) rounds and O(Δ) total bits of communication per update in the Massively Parallel Computation (MPC) model with n machines and O(n) words of memory per machine. The aforementioned algorithms require at most one adjustment, that is, a move of one vertex from one side of the cut to the other.
We also give the following fully dynamic sequential algorithms: i) a deterministic O(m^{1/2}) amortized update time algorithm where m denotes the maximum number of edges in G during any sequence of updates and, ii) a randomized algorithm which takes Õ(n^{2/3}) worst-case update time when edge updates come from an oblivious adversary.

Omer Wasim and Valerie King. Fully Dynamic Sequential and Distributed Algorithms for MAX-CUT. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 33:1-33:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{wasim_et_al:LIPIcs.FSTTCS.2020.33, author = {Wasim, Omer and King, Valerie}, title = {{Fully Dynamic Sequential and Distributed Algorithms for MAX-CUT}}, booktitle = {40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)}, pages = {33:1--33:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-174-0}, ISSN = {1868-8969}, year = {2020}, volume = {182}, editor = {Saxena, Nitin and Simon, Sunil}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.33}, URN = {urn:nbn:de:0030-drops-132746}, doi = {10.4230/LIPIcs.FSTTCS.2020.33}, annote = {Keywords: data structures, dynamic graph algorithms, approximate maximum cut, distributed computing, parallel computing} }

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**Published in:** LIPIcs, Volume 179, 34th International Symposium on Distributed Computing (DISC 2020)

The last decade has seen substantial progress on designing Byzantine agreement algorithms which do not require all-to-all communication. However, these protocols do require each node to play a particular role determined by its ID. Motivated by the rise of permissionless systems such as Bitcoin, where nodes can join and leave at will, we extend this research to a more practical model where initially, each node does not know the identity of its neighbors. In particular, a node can send to new destinations only by sending to random (or arbitrary) nodes, or responding to messages received from those destinations. We assume a synchronous and fully-connected network, with a full-information, but static Byzantine adversary. A major drawback of existing Byzantine protocols in this setting is that they have at least Ω(n²) message complexity, where n is the total number of nodes. In particular, the communication cost incurred by the honest nodes is Ω(n²), even when Byzantine node send no messages. In this paper, we design protocols for fundamental problems which are message-competitive, i.e., the total number of bits sent by honest nodes is not significantly more than the total sent by Byzantine nodes.
We describe a message-competitive algorithm to solve Byzantine agreement, leader election, and committee election. Our algorithm sends an expected O((T+n)log n) bits and has latency O(polylog(n)) (even in the CONGEST model), where T = O(n²) is the number of bits sent by Byzantine nodes. The algorithm is resilient to (1/4-ε)n Byzantine nodes for any fixed ε > 0, and succeeds with high probability. Our message bounds are essentially optimal up to polylagarithmic factors, for algorithms that run in polylogarithmic rounds in the CONGEST model.
We also show lower bounds for message-competitive Byzantine agreement regardless of rounds. We prove that, in general, one cannot hope to design Byzantine protocols that have communication cost that is significantly smaller than the cost of the Byzantine adversary.

John Augustine, Valerie King, Anisur Rahaman Molla, Gopal Pandurangan, and Jared Saia. Scalable and Secure Computation Among Strangers: Message-Competitive Byzantine Protocols. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{augustine_et_al:LIPIcs.DISC.2020.31, author = {Augustine, John and King, Valerie and Molla, Anisur Rahaman and Pandurangan, Gopal and Saia, Jared}, title = {{Scalable and Secure Computation Among Strangers: Message-Competitive Byzantine Protocols}}, booktitle = {34th International Symposium on Distributed Computing (DISC 2020)}, pages = {31:1--31:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-168-9}, ISSN = {1868-8969}, year = {2020}, volume = {179}, editor = {Attiya, Hagit}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.31}, URN = {urn:nbn:de:0030-drops-131093}, doi = {10.4230/LIPIcs.DISC.2020.31}, annote = {Keywords: Byzantine protocols, Byzantine agreement, Leader election, Committee election, Message-competitive protocol, Randomized protocol} }

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Brief Announcement

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

Building a spanning tree, minimum spanning tree (MST), and BFS tree in a distributed network are fundamental problems which are still not fully understood in terms of time and communication cost. The first work to succeed in computing a spanning tree with communication sublinear in the number of edges in an asynchronous CONGEST network appeared in DISC 2018. That algorithm which constructs an MST is sequential in the worst case; its running time is proportional to the total number of messages sent. Our paper matches its message complexity but brings the running time down to linear in n. Our techniques can also be used to provide an asynchronous algorithm with sublinear communication to construct a tree in which the distance from a source to each node is within an additive term of sqrt{n} of its actual distance.

Ali Mashreghi and Valerie King. Brief Announcement: Faster Asynchronous MST and Low Diameter Tree Construction with Sublinear Communication. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 49:1-49:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{mashreghi_et_al:LIPIcs.DISC.2019.49, author = {Mashreghi, Ali and King, Valerie}, title = {{Brief Announcement: Faster Asynchronous MST and Low Diameter Tree Construction with Sublinear Communication}}, booktitle = {33rd International Symposium on Distributed Computing (DISC 2019)}, pages = {49:1--49:3}, 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.2019.49}, URN = {urn:nbn:de:0030-drops-113566}, doi = {10.4230/LIPIcs.DISC.2019.49}, annote = {Keywords: Distributed Computing, Minimum Spanning Tree, Broadcast Tree} }

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

We provide the first asynchronous distributed algorithms to compute broadcast and minimum spanning tree with o(m) bits of communication, in a sufficiently dense graph with n nodes and m edges. For decades, it was believed that Omega(m) bits of communication are required for any algorithm that constructs a broadcast tree. In 2015, King, Kutten and Thorup showed that in the KT1 model where nodes have initial knowledge of their neighbors' identities it is possible to construct MST in O~(n) messages in the synchronous CONGEST model. In the CONGEST model messages are of size O(log n). However, no algorithm with o(m) messages were known for the asynchronous case. Here, we provide an algorithm that uses O(n^{3/2} log^{3/2} n) messages to find MST in the asynchronous CONGEST model. Our algorithm is randomized Monte Carlo and outputs MST with high probability. We will provide an algorithm for computing a spanning tree with O(n^{3/2} log^{3/2} n) messages. Given a spanning tree, we can compute MST with O~(n) messages.

Ali Mashreghi and Valerie King. Broadcast and Minimum Spanning Tree with o(m) Messages in the Asynchronous CONGEST Model. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 37:1-37:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{mashreghi_et_al:LIPIcs.DISC.2018.37, author = {Mashreghi, Ali and King, Valerie}, title = {{Broadcast and Minimum Spanning Tree with o(m) Messages in the Asynchronous CONGEST Model}}, booktitle = {32nd International Symposium on Distributed Computing (DISC 2018)}, pages = {37:1--37:17}, 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.2018.37}, URN = {urn:nbn:de:0030-drops-98263}, doi = {10.4230/LIPIcs.DISC.2018.37}, annote = {Keywords: Distributed Computing, Minimum Spanning Tree, Broadcast Tree} }

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