6 Search Results for "Dory, Michal"

Document
DOI: 10.4230/LIPIcs.DISC.2022.32
Õptimal Dual Vertex Failure Connectivity Labels

Authors: Merav Parter and Asaf Petruschka

Published in: LIPIcs, Volume 246, 36th International Symposium on Distributed Computing (DISC 2022)

Abstract
In this paper we present succinct labeling schemes for supporting connectivity queries under vertex faults. For a given n-vertex graph G, an f-VFT (resp., EFT) connectivity labeling scheme is a distributed data structure that assigns each of the graph edges and vertices a short label, such that given the labels of a vertex pair u and v, and the labels of at most f failing vertices (resp., edges) F, one can determine if u and v are connected in G ⧵ F. The primary complexity measure is the length of the individual labels. Since their introduction by [Courcelle, Twigg, STACS '07], FT labeling schemes have been devised only for a limited collection of graph families. A recent work [Dory and Parter, PODC 2021] provided EFT labeling schemes for general graphs under edge failures, leaving the vertex failure case fairly open. We provide the first sublinear f-VFT labeling schemes for f ≥ 2 for any n-vertex graph. Our key result is 2-VFT connectivity labels with O(log³ n) bits. Our constructions are based on analyzing the structure of dual failure replacement paths on top of the well-known heavy-light tree decomposition technique of [Sleator and Tarjan, STOC 1981]. We also provide f-VFT labels with sub-linear length (in |V|) for any f = o(log log n), that are based on a reduction to the existing EFT labels.
Cite as

Merav Parter and Asaf Petruschka. Õptimal Dual Vertex Failure Connectivity Labels. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 32:1-32:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{parter_et_al:LIPIcs.DISC.2022.32,
  author =	{Parter, Merav and Petruschka, Asaf},
  title =	{{\~{O}ptimal Dual Vertex Failure Connectivity Labels}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{32:1--32:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-255-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{246},
  editor =	{Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.32},
  URN =		{urn:nbn:de:0030-drops-172239},
  doi =		{10.4230/LIPIcs.DISC.2022.32},
  annote =	{Keywords: Fault-Tolerance, Heavy-Light Decomposition, Labeling Schemes}
}
Document
DOI: 10.4230/LIPIcs.STACS.2021.21
Distance Computations in the Hybrid Network Model via Oracle Simulations

Authors: Keren Censor-Hillel, Dean Leitersdorf, and Volodymyr Polosukhin

Published in: LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)

Abstract
The Hybrid network model was introduced in [Augustine et al., SODA '20] for laying down a theoretical foundation for networks which combine two possible modes of communication: One mode allows high-bandwidth communication with neighboring nodes, and the other allows low-bandwidth communication over few long-range connections at a time. This fundamentally abstracts networks such as hybrid data centers, and class-based software-defined networks. Our technical contribution is a density-aware approach that allows us to simulate a set of oracles for an overlay skeleton graph over a Hybrid network. As applications of our oracle simulations, with additional machinery that we provide, we derive fast algorithms for fundamental distance-related tasks. One of our core contributions is an algorithm in the Hybrid model for computing exact weighted shortest paths from Õ(n^{1/3}) sources which completes in Õ(n^{1/3}) rounds w.h.p. This improves, in both the runtime and the number of sources, upon the algorithm of [Kuhn and Schneider, PODC ’20], which computes shortest paths from a single source in Õ(n^{2/5}) rounds w.h.p. We additionally show a 2-approximation for weighted diameter and a (1+ε)-approximation for unweighted diameter, both in Õ(n^{1/3}) rounds w.h.p., which is comparable to the ̃ Ω(n^{1/3}) lower bound of [Kuhn and Schneider, PODC ’20] for a (2-ε)-approximation for weighted diameter and an exact unweighted diameter. We also provide fast distance approximations from multiple sources and fast approximations for eccentricities.
Cite as

Keren Censor-Hillel, Dean Leitersdorf, and Volodymyr Polosukhin. Distance Computations in the Hybrid Network Model via Oracle Simulations. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 21:1-21:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{censorhillel_et_al:LIPIcs.STACS.2021.21,
  author =	{Censor-Hillel, Keren and Leitersdorf, Dean and Polosukhin, Volodymyr},
  title =	{{Distance Computations in the Hybrid Network Model via Oracle Simulations}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{21:1--21:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.21},
  URN =		{urn:nbn:de:0030-drops-136663},
  doi =		{10.4230/LIPIcs.STACS.2021.21},
  annote =	{Keywords: Distributed graph algorithms, Hybrid network model, Distance computations}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2020.28
Fast Deterministic Algorithms for Highly-Dynamic Networks

Authors: Keren Censor-Hillel, Neta Dafni, Victor I. Kolobov, Ami Paz, and Gregory Schwartzman

Published in: LIPIcs, Volume 184, 24th International Conference on Principles of Distributed Systems (OPODIS 2020)

Abstract
This paper provides an algorithmic framework for obtaining fast distributed algorithms for a highly-dynamic setting, in which arbitrarily many edge changes may occur in each round. Our algorithm significantly improves upon prior work in its combination of (1) having an O(1) amortized time complexity, (2) using only O(log{n})-bit messages, (3) not posing any restrictions on the dynamic behavior of the environment, (4) being deterministic, (5) having strong guarantees for intermediate solutions, and (6) being applicable for a wide family of tasks. The tasks for which we deduce such an algorithm are maximal matching, (degree+1)-coloring, 2-approximation for minimum weight vertex cover, and maximal independent set (which is the most subtle case). For some of these tasks, node insertions can also be among the allowed topology changes, and for some of them also abrupt node deletions.
Cite as

Keren Censor-Hillel, Neta Dafni, Victor I. Kolobov, Ami Paz, and Gregory Schwartzman. Fast Deterministic Algorithms for Highly-Dynamic Networks. In 24th International Conference on Principles of Distributed Systems (OPODIS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 184, pp. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{censorhillel_et_al:LIPIcs.OPODIS.2020.28,
  author =	{Censor-Hillel, Keren and Dafni, Neta and Kolobov, Victor I. and Paz, Ami and Schwartzman, Gregory},
  title =	{{Fast Deterministic Algorithms for Highly-Dynamic Networks}},
  booktitle =	{24th International Conference on Principles of Distributed Systems (OPODIS 2020)},
  pages =	{28:1--28:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-176-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{184},
  editor =	{Bramas, Quentin and Oshman, Rotem and Romano, Paolo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2020.28},
  URN =		{urn:nbn:de:0030-drops-135138},
  doi =		{10.4230/LIPIcs.OPODIS.2020.28},
  annote =	{Keywords: dynamic distributed algorithms}
}
Document
DOI: 10.4230/LIPIcs.DISC.2019.30
Small Cuts and Connectivity Certificates: A Fault Tolerant Approach

Authors: Merav Parter

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

Abstract
We revisit classical connectivity problems in the {CONGEST} model of distributed computing. By using techniques from fault tolerant network design, we show improved constructions, some of which are even "local" (i.e., with O~(1) rounds) for problems that are closely related to hard global problems (i.e., with a lower bound of Omega(Diam+sqrt{n}) rounds). Distributed Minimum Cut: Nanongkai and Su presented a randomized algorithm for computing a (1+epsilon)-approximation of the minimum cut using O~(D +sqrt{n}) rounds where D is the diameter of the graph. For a sufficiently large minimum cut lambda=Omega(sqrt{n}), this is tight due to Das Sarma et al. [FOCS '11], Ghaffari and Kuhn [DISC '13]. - Small Cuts: A special setting that remains open is where the graph connectivity lambda is small (i.e., constant). The only lower bound for this case is Omega(D), with a matching bound known only for lambda <= 2 due to Pritchard and Thurimella [TALG '11]. Recently, Daga, Henzinger, Nanongkai and Saranurak [STOC '19] raised the open problem of computing the minimum cut in poly(D) rounds for any lambda=O(1). In this paper, we resolve this problem by presenting a surprisingly simple algorithm, that takes a completely different approach than the existing algorithms. Our algorithm has also the benefit that it computes all minimum cuts in the graph, and naturally extends to vertex cuts as well. At the heart of the algorithm is a graph sampling approach usually used in the context of fault tolerant (FT) design. - Deterministic Algorithms: While the existing distributed minimum cut algorithms are randomized, our algorithm can be made deterministic within the same round complexity. To obtain this, we introduce a novel definition of universal sets along with their efficient computation. This allows us to derandomize the FT graph sampling technique, which might be of independent interest. - Computation of all Edge Connectivities: We also consider the more general task of computing the edge connectivity of all the edges in the graph. In the output format, it is required that the endpoints u,v of every edge (u,v) learn the cardinality of the u-v cut in the graph. We provide the first sublinear algorithm for this problem for the case of constant connectivity values. Specifically, by using the recent notion of low-congestion cycle cover, combined with the sampling technique, we compute all edge connectivities in poly(D) * 2^{O(sqrt{log n log log n})} rounds. Sparse Certificates: For an n-vertex graph G and an integer lambda, a lambda-sparse certificate H is a subgraph H subseteq G with O(lambda n) edges which is lambda-connected iff G is lambda-connected. For D-diameter graphs, constructions of sparse certificates for lambda in {2,3} have been provided by Thurimella [J. Alg. '97] and Dori [PODC '18] respectively using O~(D) number of rounds. The problem of devising such certificates with o(D+sqrt{n}) rounds was left open by Dori [PODC '18] for any lambda >= 4. Using connections to fault tolerant spanners, we considerably improve the round complexity for any lambda in [1,n] and epsilon in (0,1), by showing a construction of (1-epsilon)lambda-sparse certificates with O(lambda n) edges using only O(1/epsilon^2 * log^{2+o(1)} n) rounds.
Cite as

Merav Parter. Small Cuts and Connectivity Certificates: A Fault Tolerant Approach. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{parter:LIPIcs.DISC.2019.30,
  author =	{Parter, Merav},
  title =	{{Small Cuts and Connectivity Certificates: A Fault Tolerant Approach}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{30:1--30:16},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.30},
  URN =		{urn:nbn:de:0030-drops-113371},
  doi =		{10.4230/LIPIcs.DISC.2019.30},
  annote =	{Keywords: Connectivity, Minimum Cut, Spanners}
}
Document
Track C: Foundations of Networks and Multi-Agent Systems: Models, Algorithms and Information Management
DOI: 10.4230/LIPIcs.ICALP.2019.135
Distributed Reconfiguration of Maximal Independent Sets

Authors: Keren Censor-Hillel and Mikaël Rabie

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
In this paper, we investigate a distributed maximal independent set (MIS) reconfiguration problem, in which there are two maximal independent sets for which every node is given its membership status, and the nodes need to communicate with their neighbors in order to find a reconfiguration schedule that switches from the first MIS to the second. Such a schedule is a list of independent sets that is restricted by forbidding two neighbors to change their membership status at the same step. In addition, these independent sets should provide some covering guarantee. We show that obtaining an actual MIS (and even a 3-dominating set) in each intermediate step is impossible. However, we provide efficient solutions when the intermediate sets are only required to be independent and 4-dominating, which is almost always possible, as we fully characterize. Consequently, our goal is to pin down the tradeoff between the possible length of the schedule and the number of communication rounds. We prove that a constant length schedule can be found in O(MIS+R32) rounds, where MIS is the complexity of finding an MIS in a worst-case graph and R32 is the complexity of finding a (3,2)-ruling set. For bounded degree graphs, this is O(log^*n) rounds and we show that it is necessary. On the other extreme, we show that with a constant number of rounds we can find a linear length schedule.
Cite as

Keren Censor-Hillel and Mikaël Rabie. Distributed Reconfiguration of Maximal Independent Sets. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 135:1-135:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{censorhillel_et_al:LIPIcs.ICALP.2019.135,
  author =	{Censor-Hillel, Keren and Rabie, Mika\"{e}l},
  title =	{{Distributed Reconfiguration of Maximal Independent Sets}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{135:1--135:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.135},
  URN =		{urn:nbn:de:0030-drops-107111},
  doi =		{10.4230/LIPIcs.ICALP.2019.135},
  annote =	{Keywords: distributed graph algorithms, reconfiguration, maximal independent set}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2017.21
Fast Distributed Approximation for TAP and 2-Edge-Connectivity

Authors: Keren Censor-Hillel and Michal Dory

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

Abstract
The tree augmentation problem (TAP) is a fundamental network design problem, in which the input is a graph G and a spanning tree T for it, and the goal is to augment T with a minimum set of edges Aug from G, such that T ∪ Aug is 2-edge-connected. TAP has been widely studied in the sequential setting. The best known approximation ratio of 2 for the weighted case dates back to the work of Frederickson and JáJá, SICOMP 1981. Recently, a 3/2-approximation was given for the unweighted case by Kortsarz and Nutov, TALG 2016, and recent breakthroughs by Adjiashvili, SODA 2017, and by Fiorini et al., 2017, give approximations better than 2 for bounded weights. In this paper, we provide the first fast distributed approximations for TAP. We present a distributed 2-approximation for weighted TAP which completes in O(h) rounds, where h is the height of T . When h is large, we show a much faster 4-approximation algorithm for the unweighted case, completing in O(D + (√n) log^{*} n) rounds, where n is the number of vertices and D is the diameter of G. Immediate consequences of our results are an O(D)-round 2-approximation algorithm for the minimum size 2-edge-connected spanning subgraph, which significantly improves upon the running time of previous approximation algorithms, and an O(hMST + (√n)log^{*} n)-round 3- approximation algorithm for the weighted case, where hMST is the height of the MST of the graph. Additional applications are algorithms for verifying 2-edge-connectivity and for augment- ing the connectivity of any connected spanning subgraph to 2. Finally, we complement our study with proving lower bounds for distributed approximations of TAP.
Cite as

Keren Censor-Hillel and Michal Dory. Fast Distributed Approximation for TAP and 2-Edge-Connectivity. In 21st International Conference on Principles of Distributed Systems (OPODIS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 95, pp. 21:1-21:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{censorhillel_et_al:LIPIcs.OPODIS.2017.21,
  author =	{Censor-Hillel, Keren and Dory, Michal},
  title =	{{Fast Distributed Approximation for TAP and 2-Edge-Connectivity}},
  booktitle =	{21st International Conference on Principles of Distributed Systems (OPODIS 2017)},
  pages =	{21:1--21:20},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2017.21},
  URN =		{urn:nbn:de:0030-drops-86475},
  doi =		{10.4230/LIPIcs.OPODIS.2017.21},
  annote =	{Keywords: approximation algorithms, distributed network design, connectivity augmentation}
}
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