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检索条件"任意字段=Proceedings of the 2013 ACM symposium on Principles of distributed computing"

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Compact distributed Certification of Planar Graphs 20

Compact Distributed Certification of Planar Graphs

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39th symposium on principles of distributed computing

作者： Feuilloley, Laurent Fraigniaud, Pierre Montealegre, Pedro Rapaport, Ivan Remila, Eric Todinca, Ioan Univ Chile Dept Ingn Ind Santiago Chile Univ Paris Paris France CNRS Paris France Univ Adolfo Ibanez Fac Ingn & Ciencias Santiago Chile Univ Chile DIM CMM UMI 2807 CNRS Santiago Chile UJM St Etienne GATE Lyon St Etienne CNRS UMR 5824 St Etienne France Univ dOrleans LIFO Orleans France INSA Ctr Val de Loire Blois Loir & Cher France

ISBN: (纸本)9781450375825

Naor, Parter, and Yogev (SODA 2020) have recently demonstrated the existence of a distributed interactive proof for planarity (i.e., for certifying that a network is planar), using a sophisticated generic technique for constructing distributed IP protocols based on sequential IP protocols. The interactive proof for planarity is based on a distributed certification of the correct execution of any given sequential linear-time algorithm for planarity testing. It involves three interactions between the prover and the randomized distributed verifier (i.e., it is a dMAM protocol), and uses small certificates, on O(logn) bits in n-node networks. We show that a single interaction from the prover suffices, and randomization is unecessary, by providing an explicit description of a proof-labeling scheme for planarity, still using certificates on just O(logn) bits. We also show that there are no proof-labeling schemes - in fact, even no locally checkable proofs - for planarity using certificates on o(logn) bits.

关键词： distributed graph algorithms communication networks fault-tolerance

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Generalizing the Sharp Threshold Phenomenon for the distributed Complexity of the Lovasz Local Lemma 20

Generalizing the Sharp Threshold Phenomenon for the Distribu...

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39th symposium on principles of distributed computing

作者： Brandt, Sebastian Grunau, Christoph Rozhon, Vaclav Swiss Fed Inst Technol Zurich Switzerland

ISBN: (纸本)9781450375825

Recently, Brandt, Maus and Uitto [PODC'19] showed that, in a restricted setting, the dependency of the complexity of the distributed Lovasz Local Lemma (LLL) on the chosen LLL criterion exhibits a sharp threshold phenomenon: They proved that, under the LLL criterion p2(d) < 1, if each random variable affects at most 3 events, the deterministic complexity of the LLL in the LOCAL model is O(d(2) + log* n). In stark contrast, under the criterion p2(d) <= 1, there is a randomized lower bound of O(log logn) by Brandt et al. [STOC'16] and a deterministic lower bound of O(logn) by Chang, Kopelowitz and Pettie [FOCS'16]. Brandt, Maus and Uitto conjectured that the same behavior holds for the unrestricted setting where each random variable affects arbitrarily many events. We prove their conjecture, by providing an algorithm that solves the LLL in time O(d(2) + log* n) under the LLL criterion p2(d) < 1, which is tight in bounded-degree graphs due to an Omega(log* n) lower bound by Chung, Pettie and Su [PODC'14]. By the work of Brandt, Maus and Uitto, obtaining such an algorithm can be reduced to proving that all members in a certain family of functions in arbitrarily high dimensions are convex on some specific domain. Unfortunately, an analytical description of these functions is known only for dimension at most 3, which led to the aforementioned restriction of their result. While obtaining those descriptions for functions of (substantially) higher dimension seems out of the reach of current techniques, we show that their convexity can be inferred by combinatorial means.

关键词： Lovasz Local Lemma LOCAL model exponential criterion sharp threshold phenomenon

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distributed Construction of Light Networks 20

Distributed Construction of Light Networks

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39th symposium on principles of distributed computing

作者： Elkin, Michael Filtser, Arnold Neiman, Ofer Ben Gurion Univ Negev Beer Sheva Israel Columbia Univ New York NY 10027 USA

ISBN: (纸本)9781450375825

A t -spanner H of a weighted graph G = (V, E, w) is a subgraph that approximates all pairwise distances up to a factor of t. The lightness of H is defined as the ratio between the weight of H to that of the minimum spanning tree. An (alpha, beta)-Shallow Light Tree (SLT) is a tree of lightness beta, that approximates all distances from a designated root vertex up to a factor of alpha. A long line of works resulted in efficient algorithms that produce (nearly) optimal light spanners and SLTs. Some of the most notable algorithmic applications of light spanners and SLTs are in distributed settings. Surprisingly, so far there are no known efficient distributed algorithms for constructing these objects in general graphs. In this paper we devise efficient distributed algorithms in the CONGEST model for constructing light spanners and SLTs, with near optimal parameters. Specifically, for any k >= 1 and 0 < epsilon < 1, we show a (2k - 1) center dot (1 + epsilon)-spanner with lightnessO( k center dot n(1/k)) can be built in (O) over tilde (n 1/2 + 1/4k+2 + D) rounds (where n = |V | and D is the hop-diameter of G). In addition, for any alpha > 1 we provide an (alpha, 1 + O(1)/a-1)-SLT in (root n + D) center dot n(o(1)) rounds. The running times of our algorithms cannot be substantially improved. We also consider spanners for the family of doubling graphs, and devise a (root n + D) center dot n(o(1)) rounds algorithm in the CONGEST model that computes a (1 + epsilon)-spanner with lightness (logn)/epsilon(O(1)). As a stepping stone, which is interesting in its own right, we first develop a distributed algorithm for constructing nets (for arbitrary weighted graphs), generalizing previous algorithms that worked only for unweighted graphs.

关键词： CONGEST Light Spanners Shallow light tree Doubling Dimension

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distributed Computation and Reconfiguration in Actively Dynamic Networks 20

Distributed Computation and Reconfiguration in Actively Dyna...

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39th symposium on principles of distributed computing

作者： Michail, Othon Skretas, George Spirakis, Paul G. Univ Liverpool Dept Comp Sci Liverpool Merseyside England Univ Patras Comp Engn & Informat Dept Patras Greece

ISBN: (纸本)9781450375825

In this paper, we study systems of distributed entities that can actively modify their communication network. This gives rise to distributed algorithms that apart from communication can also exploit network reconfiguration in order to carry out a given task. At the same time, the distributed task itself may now require a global reconfiguration from a given initial network G(s). to a target network G(f). from a family of networks having some good properties, like small diameter. To formally capture costs associated with creating and maintaining connections, we define three reasonable edge-complexity measures: the total edge activations, the maximum activated edges per round, and the maximum activated degree of a node. We give (poly)log(n) time algorithms for the general task of transforming any G(s) into a G(f) of diameter (poly)log(n), while minimizing the edge-complexity. There is a natural trade-off between time and edge complexity. Our main lower bound shows that Omega(n) total edge activations and O(n/log n) activations per round must be paid by any algorithm (even centralized) that achieves an optimum of Theta( log n) rounds. On the positive side, we give three distributed algorithms for our general task. The first runs in O( log n) time, with at most 2n active edges per round, a total of O(n log n) edge activations, a maximum degree n - 1, and a target network of diameter 2. The second achieves bounded degree by paying an additional logarithmic factor in time and in total edge activations. It gives a target network of diameter O( log n) and uses O (n) active edges per round. Our third algorithm shows that if we slightly increase the maximum degree to polylog(n) then we can achieve a running time of o (log(2) n). This novel model of distributed computation and reconfiguration in actively dynamic networks and the proposed measures of the edge complexity of distributed algorithms, may open new avenues for research in the algorithmic theory of dynamic networks.

关键词： distributed algorithms dynamic networks reconfiguration transformation polylogarithmic time edge complexity

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Genuinely distributed Byzantine Machine Learning 20

Genuinely Distributed Byzantine Machine Learning

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39th symposium on principles of distributed computing

作者： El-Mhamdi, El-Mahdi Guerraoui, Rachid Guirguis, Arsany Le Nguyen Hoang Rouault, Sebastien Ecole Polytech Fed Lausanne Lausanne VD Switzerland

ISBN: (纸本)9781450375825

Machine Learning (ML) solutions are nowadays distributed, according to the so-called server/worker architecture. One server holds the model parameters while several workers train the model. Clearly, such architecture is prone to various types of component failures, which can be all encompassed within the spectrum of a Byzantine behavior. Several approaches have been proposed recently to tolerate Byzantine workers. Yet all require trusting a central parameter server. We initiate in this paper the study of the "general" Byzantineresilient distributed machine learning problem where no individual component is trusted. In particular, we distribute the parameter server computation on several nodes. We show that this problem can be solved in an asynchronous system, despite the presence of 1/3 Byzantine parameter servers and 1/3 Byzantine workers (which is optimal). We present a new algorithm, ByzSGD, which solves the general Byzantine-resilient distributed machine learning problem by relying on three major schemes. The first, Scatter/Gather, is a communication scheme whose goal is to bound the maximum drift among models on correct servers. The second, distributed Median Contraction (DMC), leverages the geometric properties of the median in high dimensional spaces to bring parameters within the correct servers back close to each other, ensuring learning convergence. The third, Minimum-Diameter Averaging (MDA), is a statistically-robust gradient aggregation rule whose goal is to tolerate Byzantine workers. MDA requires loose bound on the variance of non-Byzantine gradient estimates, compared to existing alternatives (e.g., Krum [12]). Interestingly, ByzSGD ensures Byzantine resilience without adding communication rounds (on a normal path), compared to vanilla non-Byzantine alternatives. ByzSGD requires, however, a larger number of messages which, we show, can be reduced if we assume synchrony. We implemented ByzSGD on top of TensorFlow, and we report on our evaluation result

关键词： distributed machine learning Byzantine fault tolerance Byzantine parameter servers

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computing Shortest Paths and Diameter in the Hybrid Network Model 20

Computing Shortest Paths and Diameter in the Hybrid Network ...

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39th symposium on principles of distributed computing

作者： Kuhn, Fabian Schneider, Philipp Univ Freiburg Freiburg Germany

ISBN: (纸本)9781450375825

The HYBRID model, introduced in [Augustine et al., SODA '20], provides a theoretical foundation for networks that allow multiple communication modes. The model follows the principles of synchronous message passing, whereas nodes are allowed to use two fundamentally different communication modes. First, a local mode where nodes may exchange arbitrary information per round over edges of a local communication graph G (akin to the LOCAL model). Second, a global mode where every node may exchange O(log n) messages of size O(log n) bits per round with arbitrary nodes in the network. The HYBRID model intends to reflect the conditions of many real hybrid networks, where high-bandwidth but inherently local communication is combined with highly flexible global communication with restricted bandwidth. We continue to explore the power and limitations of the HYBRID model by investigating the complexity of computing shortest paths and diameter of the local communication graph G. We show that the all pair shortest paths problem can be solved exactly in (O) over tilde(root n) rounds, which improves on the previous (O) over tilde (n(2/3)) round algorithm and closes the gap to the known (Omega) over tilde(root n) lower bound (up to polylog n factors). Furthermore, we give constant approximations for the k-source shortest paths problem (k-SSP) with runtime (O) over tilde(root k), provided that k is sufficiently large. As k-SSP has a lower bound of (Omega) over tilde(root k) even for large approximation ratios, our k-SSP algorithms are almost tight for large enough k. In the case of a single source we give an exact (O) over tilde (n(2/5))-round algorithm, improving on the known (O) over tilde(root D)-round algorithm for graphs with large diameter D. For the diameter problem we provide algorithms with complexities (O) over tilde (n(1/3) /epsilon) and (O) over tilde (n(0.397) /epsilon) and approximation factors (3/2+epsilon) and (1+epsilon), respectively. On the negative side, we demonst

关键词： Message passing

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The Energy Complexity of BFS in Radio Networks 20

The Energy Complexity of BFS in Radio Networks

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39th symposium on principles of distributed computing

作者： Chang, Yi-Jun Dani, Varsha Hayes, Thomas P. Pettie, Seth Swiss Fed Inst Technol Zurich Switzerland Univ New Mexico Albuquerque NM USA Univ Michigan Ann Arbor MI 48109 USA

ISBN: (纸本)9781450375825

We consider a model of energy complexity in Radio Networks in which transmitting or listening on the channel costs one unit of energy and computation is free. This simplified model captures key aspects of battery-powered sensors: that battery-life is most influenced by transceiver usage, and that at low transmission powers, the actual cost of transmitting and listening are very similar. The energy complexity of tasks in single-hop (clique) networks are well understood [6, 9, 20, 32]. Recent work of Chang et al. [8] considered energy complexity in multi-hop networks and showed that Broadcast admits an energy-efficient protocol, by which we mean each of the n nodes in the network spends O(polylog(n)) energy. This work left open the strange possibility that all natural problems in multi-hop networks might admit such an energyefficient solution. In this paper we prove that the landscape of energy complexity is rich enough to support a multitude of problem complexities. Whereas Broadcast can be solved by an energy-efficient protocol, exact computation of Diameter cannot, requiring Omega(n) energy. Our main result is that BreadthFirstSearch has sub-polynomial energy complexity at most 2(O)((root log n log log n)) = n(o(1));whether it admits an efficient O(polylog(n))-energy protocol is an open problem. Our main algorithm involves recursively solving a generalized BFS problem on a "cluster graph" introduced by Miller, Peng, and Xu [31]. In this application, we make crucial use of a close relationship between distances in this cluster graph, and distances in the original network. This relationship is new and may be of independent interest. We also consider the problem of approximating the network Diameter. From our main result, it is immediate that Diameter can be 2-approximated using no(1) energy per node. We observe that, for all epsilon > 0, approximating Diameter to within a (2 - epsilon) factor requires Omega(n) energy per node. However, this lower bound is only due to

关键词： distributed computing graph algorithms energy-aware computing radio networks sensor networks

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Differential Privacy in distributed Environments: An Overview and Open Questions 21

Differential Privacy in Distributed Environments: An Overvie...

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proceedings of the 2021 acm symposium on principles of distributed computing

作者： Cynthia Dwork Harvard University & Radcliffe Institute for Advanced Study Cambridge MA USA

ISBN: (纸本)9781450385480

Differential privacy is a mathematically rigorous definition of privacy tailored to statistical analysis of large datasets. Differentially private algorithms are equipped with a parameter which controls the formal measure of privacy loss. All algorithms have utility/privacy tradeoffs, and the goal of algorithmic research in differential privacy is to optimize this *** privacy is most widely studied in the centralized model, in which a trusted and trustworthy curator has access to raw data. Deployment in industry has focused on the local model, where privacy is "rolled into" the data on the client via randomization before being collected. There is a separation between the power of the centralized and local *** a brief recap of differential privacy and its properties, we will survey a few highlights of differential privacy in a variety of distributed settings that lie between the local and centralized models, and conclude with suggestions for future research.

关键词： differential privacy distributed algorithms

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On distributed Listing of Cliques 20

On Distributed Listing of Cliques

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39th symposium on principles of distributed computing

作者： Censor-Hillel, Keren Le Gall, Francois Leitersdorf, Dean Technion Dept Comp Sci Haifa Israel Nagoya Univ Grad Sch Math Nagoya Aichi Japan

ISBN: (纸本)9781450375825

We show an (O) over tilde (n(p/(p+2)))-round algorithm in the CONGEST model for listing of K-p (a clique with p nodes), for all p = 4, p >= 6. For p = 5, we show an (O) over tilde (n(3/4))-round algorithm. For p = 4 and p = 5, our results improve upon the previous state-of-the-art of O(n(5/6+o(1))) and O(n(21/22+o(1))), respectively, by Eden et al. [DISC 2019]. For all p >= 6, ours is the first sub-linear round algorithm for Kp listing. We leverage the recent expander decomposition algorithm of Chang et al. [SODA 2019] to create clusters with a good mixing time. Three key novelties in our algorithm are: (1) we carefully iterate our listing process with coupled values of min-degree within the clusters and arboricity outside the clusters, (2) all the listing is done within the cluster, which necessitates new techniques for bringing into the cluster the information about all edges that can potentially form K-p instances with the cluster edges, and (3) within each cluster we use a sparsity-aware listing algorithm, which is faster than a general listing algorithm and which we can allow the cluster to use since we make sure to sparsify the graph as the iterations proceed. As a byproduct of our algorithm, we show an optimal sparsityaware algorithm for K-p listing, which runs in Theta(1 + m/n(1+2/p)) rounds in the CONGESTED CLIQUE model. Previously, Pandurangan et al. [SPAA 2018], Chang et al. [SODA 2019], and Censor-Hillel et al. [TCS 2020] showed sparsity-aware algorithms for the case of p = 3, yet ours is the first such sparsity aware algorithm for p >= 4.

关键词： Clustering algorithms

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A deterministic almost-tight distributed algorithm for approximating single-source shortest paths

A deterministic almost-tight distributed algorithm for appro...

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作者： Henzinger, Monika Krinninger, Sebastian Nanongkai, Danupon Faculty of Computer Science University of Vienna Vienna1090 Austria Department of Computer Sciences University of Salzburg Salzburg5020 Austria Department of Theoretical Computer Science KTH Royal Institute of Technology Stockholm10044 Sweden

We present a deterministic (1 + o(1))-approximation (n1/2+o(1) + D1+o(1))-time algorithm for solving the single-source shortest paths problem on distributed weighted networks (the CONGEST model);here n is the number of nodes in the network, D is its (hop) diameter, and edge weights are positive integers from 1 to poly(n). This is the first nontrivial deterministic algorithm for this problem. It also improves (i) the running time of the randomized (1 + o(1))-approximation Õ(√nD1/4 + D)-time algorithm of Nanongkai [in proceedings of STOC, 2014, pp. 565-573] by a factor of as large as n1/8, and (ii) the O(∊-1 log ∊ -1)-approximation factor of Lenzen and Patt-Shamir's Õ(n1/2+∊ + D)-time algorithm [in proceedings of STOC, 2013, pp. 381-390] within the same running time. (Throughout, we use Õ(·) to hide polylogarithmic factors in n.) Our running time matches the known time lower bound of Ω (√n/log n + D) [M. Elkin, SIAM J. Comput., 36 (2006), pp. 433-456], thus essentially settling the status of this problem which was raised at least a decade ago [M. Elkin, SIGACT News, 35 (2004), pp. 40-57]. It also implies a (2 + o(1))-approximation (n1/2+o(1) + D1+o(1))- time algorithm for approximating a network's weighted diameter which almost matches the lower bound by Holzer and Pinsker [in proceedings of OPODIS, 2015, Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, Germany, 2016, 6]. In achieving this result, we develop two techniques which might be of independent interest and useful in other settings: (i) a deterministic process that replaces the ``hitting set argument"" commonly used for shortest paths computation in various settings, and (ii) a simple, deterministic construction of an (no(1), o(1))-hop set of size n1+o(1). We combine these techniques with many distributed algorithmic techniques, some of which are from problems that are not directly related to shortest paths, e.g., ruling sets [A. V. Goldberg, S. A. Plotkin, and G. E. Shannon, SIAM J. Discrete Math., 1 (1988),

关键词： Approximation algorithms

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