Document

**Published in:** LIPIcs, Volume 217, 25th International Conference on Principles of Distributed Systems (OPODIS 2021)

Let G be a graph on n nodes. In the stochastic population protocol model, a collection of n indistinguishable, resource-limited nodes collectively solve tasks via pairwise interactions. In each interaction, two randomly chosen neighbors first read each other’s states, and then update their local states. A rich line of research has established tight upper and lower bounds on the complexity of fundamental tasks, such as majority and leader election, in this model, when G is a clique. Specifically, in the clique, these tasks can be solved fast, i.e., in n polylog n pairwise interactions, with high probability, using at most polylog n states per node.
In this work, we consider the more general setting where G is an arbitrary regular graph, and present a technique for simulating protocols designed for fully-connected networks in any connected regular graph. Our main result is a simulation that is efficient on many interesting graph families: roughly, the simulation overhead is polylogarithmic in the number of nodes, and quadratic in the conductance of the graph. As a sample application, we show that, in any regular graph with conductance φ, both leader election and exact majority can be solved in φ^{-2} ⋅ n polylog n pairwise interactions, with high probability, using at most φ^{-2} ⋅ polylog n states per node. This shows that there are fast and space-efficient population protocols for leader election and exact majority on graphs with good expansion properties. We believe our results will prove generally useful, as they allow efficient technology transfer between the well-mixed (clique) case, and the under-explored spatial setting.

Dan Alistarh, Rati Gelashvili, and Joel Rybicki. Fast Graphical Population Protocols. In 25th International Conference on Principles of Distributed Systems (OPODIS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 217, pp. 14:1-14:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{alistarh_et_al:LIPIcs.OPODIS.2021.14, author = {Alistarh, Dan and Gelashvili, Rati and Rybicki, Joel}, title = {{Fast Graphical Population Protocols}}, booktitle = {25th International Conference on Principles of Distributed Systems (OPODIS 2021)}, pages = {14:1--14:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-219-8}, ISSN = {1868-8969}, year = {2022}, volume = {217}, editor = {Bramas, Quentin and Gramoli, Vincent and Milani, Alessia}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2021.14}, URN = {urn:nbn:de:0030-drops-157897}, doi = {10.4230/LIPIcs.OPODIS.2021.14}, annote = {Keywords: population protocols, leader election, exact majority, graphs} }

Document

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

This paper gives tight logarithmic lower bounds on the solo step complexity of leader election in an asynchronous shared-memory model with single-writer multi-reader (SWMR) registers, for both deterministic and randomized obstruction-free algorithms. The approach extends to lower bounds for deterministic and randomized obstruction-free algorithms using multi-writer registers under bounded write concurrency, showing a trade-off between the solo step complexity of a leader election algorithm, and the worst-case number of stalls incurred by a processor in an execution.

Dan Alistarh, Rati Gelashvili, and Giorgi Nadiradze. Lower Bounds for Shared-Memory Leader Election Under Bounded Write Contention. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 4:1-4:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{alistarh_et_al:LIPIcs.DISC.2021.4, author = {Alistarh, Dan and Gelashvili, Rati and Nadiradze, Giorgi}, title = {{Lower Bounds for Shared-Memory Leader Election Under Bounded Write Contention}}, booktitle = {35th International Symposium on Distributed Computing (DISC 2021)}, pages = {4:1--4:17}, 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.2021.4}, URN = {urn:nbn:de:0030-drops-148063}, doi = {10.4230/LIPIcs.DISC.2021.4}, annote = {Keywords: Lower Bounds, Leader Election, Shared-Memory} }

Document

Brief Announcement

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

Let G be a graph on n nodes. In the stochastic population protocol model, a collection of n indistinguishable, resource-limited nodes collectively solve tasks via pairwise interactions. In each interaction, two randomly chosen neighbors first read each other’s states, and then update their local states. A rich line of research has established tight upper and lower bounds on the complexity of fundamental tasks, such as majority and leader election, in this model, when G is a clique. Specifically, in the clique, these tasks can be solved fast, i.e., in n polylog n pairwise interactions, with high probability, using at most polylog n states per node.
In this work, we consider the more general setting where G is an arbitrary graph, and present a technique for simulating protocols designed for fully-connected networks in any connected regular graph. Our main result is a simulation that is efficient on many interesting graph families: roughly, the simulation overhead is polylogarithmic in the number of nodes, and quadratic in the conductance of the graph. As an example, this implies that, in any regular graph with conductance φ, both leader election and exact majority can be solved in φ^{-2} ⋅ n polylog n pairwise interactions, with high probability, using at most φ^{-2} ⋅ polylog n states per node. This shows that there are fast and space-efficient population protocols for leader election and exact majority on graphs with good expansion properties.

Dan Alistarh, Rati Gelashvili, and Joel Rybicki. Brief Announcement: Fast Graphical Population Protocols. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 43:1-43:4, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{alistarh_et_al:LIPIcs.DISC.2021.43, author = {Alistarh, Dan and Gelashvili, Rati and Rybicki, Joel}, title = {{Brief Announcement: Fast Graphical Population Protocols}}, booktitle = {35th International Symposium on Distributed Computing (DISC 2021)}, pages = {43:1--43:4}, 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.2021.43}, URN = {urn:nbn:de:0030-drops-148451}, doi = {10.4230/LIPIcs.DISC.2021.43}, annote = {Keywords: population protocols, leader election, majority} }

Document

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

The design and implementation of efficient concurrent data structures has seen significant attention. However, most of this work has focused on concurrent data structures providing good worst-case guarantees. In real workloads, objects are often accessed at different rates, since access distributions may be non-uniform. Efficient distribution-adaptive data structures are known in the sequential case, e.g. the splay-trees; however, they often are hard to translate efficiently in the concurrent case.
In this paper, we investigate distribution-adaptive concurrent data structures, and propose a new design called the splay-list. At a high level, the splay-list is similar to a standard skip-list, with the key distinction that the height of each element adapts dynamically to its access rate: popular elements "move up," whereas rarely-accessed elements decrease in height. We show that the splay-list provides order-optimal amortized complexity bounds for a subset of operations, while being amenable to efficient concurrent implementation. Experimental results show that the splay-list can leverage distribution-adaptivity to improve on the performance of classic concurrent designs, and can outperform the only previously-known distribution-adaptive design in certain settings.

Vitaly Aksenov, Dan Alistarh, Alexandra Drozdova, and Amirkeivan Mohtashami. The Splay-List: A Distribution-Adaptive Concurrent Skip-List. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 3:1-3:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{aksenov_et_al:LIPIcs.DISC.2020.3, author = {Aksenov, Vitaly and Alistarh, Dan and Drozdova, Alexandra and Mohtashami, Amirkeivan}, title = {{The Splay-List: A Distribution-Adaptive Concurrent Skip-List}}, booktitle = {34th International Symposium on Distributed Computing (DISC 2020)}, pages = {3:1--3:18}, 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.2020.3}, URN = {urn:nbn:de:0030-drops-130818}, doi = {10.4230/LIPIcs.DISC.2020.3}, annote = {Keywords: Data structures, self-adjusting, concurrency} }

Document

Track A: Algorithms, Complexity and Games

**Published in:** LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

We consider the following dynamic load-balancing process: given an underlying graph G with n nodes, in each step t≥ 0, one unit of load is created, and placed at a randomly chosen graph node. In the same step, the chosen node picks a random neighbor, and the two nodes balance their loads by averaging them. We are interested in the expected gap between the minimum and maximum loads at nodes as the process progresses, and its dependence on n and on the graph structure.
Variants of the above graphical balanced allocation process have been studied previously by Peres, Talwar, and Wieder [Peres et al., 2015], and by Sauerwald and Sun [Sauerwald and Sun, 2015]. These authors left as open the question of characterizing the gap in the case of cycle graphs in the dynamic case, where weights are created during the algorithm’s execution. For this case, the only known upper bound is of 𝒪(n log n), following from a majorization argument due to [Peres et al., 2015], which analyzes a related graphical allocation process.
In this paper, we provide an upper bound of 𝒪 (√n log n) on the expected gap of the above process for cycles of length n. We introduce a new potential analysis technique, which enables us to bound the difference in load between k-hop neighbors on the cycle, for any k ≤ n/2. We complement this with a "gap covering" argument, which bounds the maximum value of the gap by bounding its value across all possible subsets of a certain structure, and recursively bounding the gaps within each subset. We provide analytical and experimental evidence that our upper bound on the gap is tight up to a logarithmic factor.

Dan Alistarh, Giorgi Nadiradze, and Amirmojtaba Sabour. Dynamic Averaging Load Balancing on Cycles. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 7:1-7:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{alistarh_et_al:LIPIcs.ICALP.2020.7, author = {Alistarh, Dan and Nadiradze, Giorgi and Sabour, Amirmojtaba}, title = {{Dynamic Averaging Load Balancing on Cycles}}, booktitle = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)}, pages = {7:1--7:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-138-2}, ISSN = {1868-8969}, year = {2020}, volume = {168}, editor = {Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.7}, URN = {urn:nbn:de:0030-drops-124142}, doi = {10.4230/LIPIcs.ICALP.2020.7}, annote = {Keywords: Algorithms, Load Balancing} }

Document

**Published in:** LIPIcs, Volume 153, 23rd International Conference on Principles of Distributed Systems (OPODIS 2019)

Union-Find (or Disjoint-Set Union) is one of the fundamental problems in computer science; it has been well-studied from both theoretical and practical perspectives in the sequential case. Recently, there has been mounting interest in analyzing this problem in the concurrent scenario, and several asymptotically-efficient algorithms have been proposed. Yet, to date, there is very little known about the practical performance of concurrent Union-Find.
This work addresses this gap. We evaluate and analyze the performance of several concurrent Union-Find algorithms and optimization strategies across a wide range of platforms (Intel, AMD, and ARM) and workloads (social, random, and road networks, as well as integrations into more complex algorithms). We first observe that, due to the limited computational cost, the number of induced cache misses is the critical determining factor for the performance of existing algorithms. We introduce new techniques to reduce this cost by storing node priorities implicitly and by using plain reads and writes in a way that does not affect the correctness of the algorithms. Finally, we show that Union-Find implementations are an interesting application for Transactional Memory (TM): one of the fastest algorithm variants we discovered is a sequential one that uses coarse-grained locking with the lock elision optimization to reduce synchronization cost and increase scalability.

Dan Alistarh, Alexander Fedorov, and Nikita Koval. In Search of the Fastest Concurrent Union-Find Algorithm. In 23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 15:1-15:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{alistarh_et_al:LIPIcs.OPODIS.2019.15, author = {Alistarh, Dan and Fedorov, Alexander and Koval, Nikita}, title = {{In Search of the Fastest Concurrent Union-Find Algorithm}}, booktitle = {23rd International Conference on Principles of Distributed Systems (OPODIS 2019)}, pages = {15:1--15:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-133-7}, ISSN = {1868-8969}, year = {2020}, volume = {153}, editor = {Felber, Pascal and Friedman, Roy and Gilbert, Seth and Miller, Avery}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2019.15}, URN = {urn:nbn:de:0030-drops-118012}, doi = {10.4230/LIPIcs.OPODIS.2019.15}, annote = {Keywords: union-find, concurrency, evaluation, benchmarks, hardware transactional memory} }

X

Feedback for Dagstuhl Publishing

Feedback submitted

Please try again later or send an E-mail