7 Search Results for "Gonen, Tzlil"

Document
DOI: 10.4230/LIPIcs.DISC.2024.12
Faster Cycle Detection in the Congested Clique

Authors: Keren Censor-Hillel, Tomer Even, and Virginia Vassilevska Williams

Published in: LIPIcs, Volume 319, 38th International Symposium on Distributed Computing (DISC 2024)

Abstract
We provide a fast distributed algorithm for detecting h-cycles in the Congested Clique model, whose running time decreases as the number of h-cycles in the graph increases. In undirected graphs, constant-round algorithms are known for cycles of even length. Our algorithm greatly improves upon the state of the art for odd values of h. Moreover, our running time applies also to directed graphs, in which case the improvement is for all values of h. Further, our techniques allow us to obtain a triangle detection algorithm in the quantum variant of this model, which is faster than prior work. A key technical contribution we develop to obtain our fast cycle detection algorithm is a new algorithm for computing the product of many pairs of small matrices in parallel, which may be of independent interest.
Cite as

Keren Censor-Hillel, Tomer Even, and Virginia Vassilevska Williams. Faster Cycle Detection in the Congested Clique. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 12:1-12:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{censorhillel_et_al:LIPIcs.DISC.2024.12,
  author =	{Censor-Hillel, Keren and Even, Tomer and Vassilevska Williams, Virginia},
  title =	{{Faster Cycle Detection in the Congested Clique}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{12:1--12:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-352-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{319},
  editor =	{Alistarh, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2024.12},
  URN =		{urn:nbn:de:0030-drops-212382},
  doi =		{10.4230/LIPIcs.DISC.2024.12},
  annote =	{Keywords: triangle detection, cycle detection, distributed computing, Congested Clique, quantum computing, Fast matrix multiplication, Fast rectangular matrix multiplication}
}
Document
DOI: 10.4230/LIPIcs.DISC.2024.25
Distributed Model Checking on Graphs of Bounded Treedepth

Authors: Fedor V. Fomin, Pierre Fraigniaud, Pedro Montealegre, Ivan Rapaport, and Ioan Todinca

Published in: LIPIcs, Volume 319, 38th International Symposium on Distributed Computing (DISC 2024)

Abstract
We establish that every monadic second-order logic (MSO) formula on graphs with bounded treedepth is decidable in a constant number of rounds within the CONGEST model. To our knowledge, this marks the first meta-theorem regarding distributed model-checking. Various optimization problems on graphs are expressible in MSO. Examples include determining whether a graph G has a clique of size k, whether it admits a coloring with k colors, whether it contains a graph H as a subgraph or minor, or whether terminal vertices in G could be connected via vertex-disjoint paths. Our meta-theorem significantly enhances the work of Bousquet et al. [PODC 2022], which was focused on distributed certification of MSO on graphs with bounded treedepth. Moreover, our results can be extended to solving optimization and counting problems expressible in MSO, in graphs of bounded treedepth.
Cite as

Fedor V. Fomin, Pierre Fraigniaud, Pedro Montealegre, Ivan Rapaport, and Ioan Todinca. Distributed Model Checking on Graphs of Bounded Treedepth. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 25:1-25:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{fomin_et_al:LIPIcs.DISC.2024.25,
  author =	{Fomin, Fedor V. and Fraigniaud, Pierre and Montealegre, Pedro and Rapaport, Ivan and Todinca, Ioan},
  title =	{{Distributed Model Checking on Graphs of Bounded Treedepth}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{25:1--25:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-352-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{319},
  editor =	{Alistarh, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2024.25},
  URN =		{urn:nbn:de:0030-drops-212513},
  doi =		{10.4230/LIPIcs.DISC.2024.25},
  annote =	{Keywords: proof-labeling schemes, local computing, CONGEST model}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.57
Stochastic Distance in Property Testing

Authors: Uri Meir, Gregory Schwartzman, and Yuichi Yoshida

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

Abstract
We introduce a novel concept termed "stochastic distance" for property testing. Diverging from the traditional definition of distance, where a distance t implies that there exist t edges that can be added to ensure a graph possesses a certain property (such as k-edge-connectivity), our new notion implies that there is a high probability that adding t random edges will endow the graph with the desired property. While formulating testers based on this new distance proves challenging in a sequential environment, it is much easier in a distributed setting. Taking k-edge-connectivity as a case study, we design ultra-fast testing algorithms in the CONGEST model. Our introduction of stochastic distance offers a more natural fit for the distributed setting, providing a promising avenue for future research in emerging models of computation.
Cite as

Uri Meir, Gregory Schwartzman, and Yuichi Yoshida. Stochastic Distance in Property Testing. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 57:1-57:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{meir_et_al:LIPIcs.APPROX/RANDOM.2024.57,
  author =	{Meir, Uri and Schwartzman, Gregory and Yoshida, Yuichi},
  title =	{{Stochastic Distance in Property Testing}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{57:1--57:13},
  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.2024.57},
  URN =		{urn:nbn:de:0030-drops-210506},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.57},
  annote =	{Keywords: Connectivity, k-edge connectivity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.60
Testing C_k-Freeness in Bounded-Arboricity Graphs

Authors: Talya Eden, Reut Levi, and Dana Ron

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We study the problem of testing C_k-freeness (k-cycle-freeness) for fixed constant k > 3 in graphs with bounded arboricity (but unbounded degrees). In particular, we are interested in one-sided error algorithms, so that they must detect a copy of C_k with high constant probability when the graph is ε-far from C_k-free. We next state our results for constant arboricity and constant ε with a focus on the dependence on the number of graph vertices, n. The query complexity of all our algorithms grows polynomially with 1/ε. 1) As opposed to the case of k = 3, where the complexity of testing C₃-freeness grows with the arboricity of the graph but not with the size of the graph (Levi, ICALP 2021) this is no longer the case already for k = 4. We show that Ω(n^{1/4}) queries are necessary for testing C₄-freeness, and that Õ(n^{1/4}) are sufficient. The same bounds hold for C₅. 2) For every fixed k ≥ 6, any one-sided error algorithm for testing C_k-freeness must perform Ω(n^{1/3}) queries. 3) For k = 6 we give a testing algorithm whose query complexity is Õ(n^{1/2}). 4) For any fixed k, the query complexity of testing C_k-freeness is upper bounded by {O}(n^{1-1/⌊k/2⌋}). The last upper bound builds on another result in which we show that for any fixed subgraph F, the query complexity of testing F-freeness is upper bounded by O(n^{1-1/𝓁(F)}), where 𝓁(F) is a parameter of F that is always upper bounded by the number of vertices in F (and in particular is k/2 in C_k for even k). We extend some of our results to bounded (non-constant) arboricity, where in particular, we obtain sublinear upper bounds for all k. Our Ω(n^{1/4}) lower bound for testing C₄-freeness in constant arboricity graphs provides a negative answer to an open problem posed by (Goldreich, 2021).
Cite as

Talya Eden, Reut Levi, and Dana Ron. Testing C_k-Freeness in Bounded-Arboricity Graphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 60:1-60:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{eden_et_al:LIPIcs.ICALP.2024.60,
  author =	{Eden, Talya and Levi, Reut and Ron, Dana},
  title =	{{Testing C\underlinek-Freeness in Bounded-Arboricity Graphs}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{60:1--60:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.60},
  URN =		{urn:nbn:de:0030-drops-202033},
  doi =		{10.4230/LIPIcs.ICALP.2024.60},
  annote =	{Keywords: Property Testing, Cycle-Freeness, Bounded Arboricity}
}
Document
DOI: 10.4230/LIPIcs.DISC.2020.33
Fast Distributed Algorithms for Girth, Cycles and Small Subgraphs

Authors: Keren Censor-Hillel, Orr Fischer, Tzlil Gonen, François Le Gall, Dean Leitersdorf, and Rotem Oshman

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

Abstract
In this paper we give fast distributed graph algorithms for detecting and listing small subgraphs, and for computing or approximating the girth. Our algorithms improve upon the state of the art by polynomial factors, and for girth, we obtain a constant-time algorithm for additive +1 approximation in Congested Clique, and the first parametrized algorithm for exact computation in Congest. In the Congested Clique model, we first develop a technique for learning small neighborhoods, and apply it to obtain an O(1)-round algorithm that computes the girth with only an additive +1 error. Next, we introduce a new technique (the partition tree technique) allowing for efficiently listing all copies of any subgraph, which is deterministic and improves upon the state-of the-art for non-dense graphs. We give two concrete applications of the partition tree technique: First we show that for constant k, it is possible to solve C_{2k}-detection in O(1) rounds in the Congested Clique, improving on prior work, which used fast matrix multiplication and thus had polynomial round complexity. Second, we show that in triangle-free graphs, the girth can be exactly computed in time polynomially faster than the best known bounds for general graphs. We remark that no analogous result is currently known for sequential algorithms. In the Congest model, we describe a new approach for finding cycles, and instantiate it in two ways: first, we show a fast parametrized algorithm for girth with round complexity Õ(min{g⋅ n^{1-1/Θ(g)},n}) for any girth g; and second, we show how to find small even-length cycles C_{2k} for k = 3,4,5 in O(n^{1-1/k}) rounds. This is a polynomial improvement upon the previous running times; for example, our C₆-detection algorithm runs in O(n^{2/3}) rounds, compared to O(n^{3/4}) in prior work. Finally, using our improved C₆-freeness algorithm, and the barrier on proving lower bounds on triangle-freeness of Eden et al., we show that improving the current ̃Ω(√n) lower bound for C₆-freeness of Korhonen et al. by any polynomial factor would imply strong circuit complexity lower bounds.
Cite as

Keren Censor-Hillel, Orr Fischer, Tzlil Gonen, François Le Gall, Dean Leitersdorf, and Rotem Oshman. Fast Distributed Algorithms for Girth, Cycles and Small Subgraphs. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 33:1-33:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{censorhillel_et_al:LIPIcs.DISC.2020.33,
  author =	{Censor-Hillel, Keren and Fischer, Orr and Gonen, Tzlil and Le Gall, Fran\c{c}ois and Leitersdorf, Dean and Oshman, Rotem},
  title =	{{Fast Distributed Algorithms for Girth, Cycles and Small Subgraphs}},
  booktitle =	{34th International Symposium on Distributed Computing (DISC 2020)},
  pages =	{33:1--33:17},
  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.2020.33},
  URN =		{urn:nbn:de:0030-drops-131115},
  doi =		{10.4230/LIPIcs.DISC.2020.33},
  annote =	{Keywords: distributed graph algorithms, cycles, girth, Congested Clique, CONGEST}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2017.6
Lower Bounds for Subgraph Detection in the CONGEST Model

Authors: Tzlil Gonen and Rotem Oshman

Published in: LIPIcs, Volume 95, 21st International Conference on Principles of Distributed Systems (OPODIS 2017)

Abstract
In the subgraph-freeness problem, we are given a constant-sized graph H, and wish to de- termine whether the network graph contains H as a subgraph or not. Until now, the only lower bounds on subgraph-freeness known for the CONGEST model were for cycles of length greater than 3; here we extend and generalize the cycle lower bound, and obtain polynomial lower bounds for subgraph-freeness in the CONGEST model for two classes of subgraphs. The first class contains any graph obtained by starting from a 2-connected graph H for which we already know a lower bound, and replacing the vertices of H by arbitrary connected graphs. We show that the lower bound on H carries over to the new graph. The second class is constructed by starting from a cycle Ck of length k ≥ 4, and constructing a graph H ̃ from Ck by replacing each edge {i, (i + 1) mod k} of the cycle with a connected graph Hi, subject to some constraints on the graphs H_{0}, . . . , H_{k−1}. In this case we obtain a polynomial lower bound for the new graph H ̃, depending on the size of the shortest cycle in H ̃ passing through the vertices of the original k-cycle.
Cite as

Tzlil Gonen and Rotem Oshman. Lower Bounds for Subgraph Detection in the CONGEST Model. In 21st International Conference on Principles of Distributed Systems (OPODIS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 95, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{gonen_et_al:LIPIcs.OPODIS.2017.6,
  author =	{Gonen, Tzlil and Oshman, Rotem},
  title =	{{Lower Bounds for Subgraph Detection in the CONGEST Model}},
  booktitle =	{21st International Conference on Principles of Distributed Systems (OPODIS 2017)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-061-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{95},
  editor =	{Aspnes, James and Bessani, Alysson and Felber, Pascal and Leit\~{a}o, Jo\~{a}o},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2017.6},
  URN =		{urn:nbn:de:0030-drops-86445},
  doi =		{10.4230/LIPIcs.OPODIS.2017.6},
  annote =	{Keywords: subgraph freeness, CONGEST, lower bounds}
}
Document
DOI: 10.4230/LIPIcs.DISC.2017.15
Three Notes on Distributed Property Testing

Authors: Guy Even, Orr Fischer, Pierre Fraigniaud, Tzlil Gonen, Reut Levi, Moti Medina, Pedro Montealegre, Dennis Olivetti, Rotem Oshman, Ivan Rapaport, and Ioan Todinca

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

Abstract
In this paper we present distributed property-testing algorithms for graph properties in the CONGEST model, with emphasis on testing subgraph-freeness. Testing a graph property P means distinguishing graphs G = (V,E) having property P from graphs that are epsilon-far from having it, meaning that epsilon|E| edges must be added or removed from G to obtain a graph satisfying P. We present a series of results, including: - Testing H-freeness in O(1/epsilon) rounds, for any constant-sized graph H containing an edge (u,v) such that any cycle in H contain either u or v (or both). This includes all connected graphs over five vertices except K_5. For triangles, we can do even better when epsilon is not too small. - A deterministic CONGEST protocol determining whether a graph contains a given tree as a subgraph in constant time. - For cliques K_s with s >= 5, we show that K_s-freeness can be tested in O(m^(1/2-1/(s-2)) epsilon^(-1/2-1/(s-2))) rounds, where m is the number of edges in the network graph. - We describe a general procedure for converting epsilon-testers with f(D) rounds, where D denotes the diameter of the graph, to work in O((log n)/epsilon)+f((log n)/epsilon) rounds, where n is the number of processors of the network. We then apply this procedure to obtain an epsilon-tester for testing whether a graph is bipartite and testing whether a graph is cycle-free. Moreover, for cycle-freeness, we obtain a corrector of the graph that locally corrects the graph so that the corrected graph is acyclic. Note that, unlike a tester, a corrector needs to mend the graph in many places in the case that the graph is far from having the property. These protocols extend and improve previous results of [Censor-Hillel et al. 2016] and [Fraigniaud et al. 2016].
Cite as

Guy Even, Orr Fischer, Pierre Fraigniaud, Tzlil Gonen, Reut Levi, Moti Medina, Pedro Montealegre, Dennis Olivetti, Rotem Oshman, Ivan Rapaport, and Ioan Todinca. Three Notes on Distributed Property Testing. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 15:1-15:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{even_et_al:LIPIcs.DISC.2017.15,
  author =	{Even, Guy and Fischer, Orr and Fraigniaud, Pierre and Gonen, Tzlil and Levi, Reut and Medina, Moti and Montealegre, Pedro and Olivetti, Dennis and Oshman, Rotem and Rapaport, Ivan and Todinca, Ioan},
  title =	{{Three Notes on Distributed Property Testing}},
  booktitle =	{31st International Symposium on Distributed Computing (DISC 2017)},
  pages =	{15:1--15:30},
  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.2017.15},
  URN =		{urn:nbn:de:0030-drops-79847},
  doi =		{10.4230/LIPIcs.DISC.2017.15},
  annote =	{Keywords: Property testing, Property correcting, Distributed algorithms, CONGEST model}
}
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