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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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Lower Bounds for distributed Sketching of Maximal Matchings and Maximal Independent Sets 20

Lower Bounds for Distributed Sketching of Maximal Matchings ...

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39th symposium on principles of distributed computing

作者： Assadi, Sepehr Kol, Gillat Oshman, Rotem Rutgers State Univ Piscataway NJ 08854 USA Princeton Univ Princeton NJ 08544 USA Tel Aviv Univ Tel Aviv Israel

ISBN: (纸本)9781450375825

Consider the following distributed graph sketching model: There is a referee and n vertices in an undirected graph G sharing public randomness. Each vertex v only knows its neighborhood in G and the referee receives no input initially. The vertices simultaneously each sends a message, called a sketch, to the referee who then based on the received sketches outputs a solution to some combinatorial problem on G, say, the minimum spanning tree problem. Previous work on graph sketching have shown that numerous problems, including connectivity, minimum spanning tree, edge or vertex connectivity, cut or spectral sparsifiers, and (Delta+1)-vertex coloring, all admit efficient algorithms in this model that only require sketches of size polylog(n) per vertex. In contrast, we prove that the two fundamental problems of maximal matching and maximal independent set do not admit such efficient solutions: Any algorithm for either problem that errs with a small constant probability requires sketches of size Omega(n(1/2-epsilon)) for any constant epsilon > 0. We prove our results by analyzing communication complexity of these problems in a communication model that allows sharing of inputs between limited number of players, and hence lies between the standard number-in-hand and number-on-forehead multi-party communication models. Our proofs are based on a family of hard instances using Ruzsa-Szemeredi graphs and information-theoretic arguments to establish the communication lower bounds.

关键词： distributed sketching maximal matching maximal independent set communication complexity broadcast congested clique

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DConstructor: Efficient and Robust Network Construction with Polylogarithmic Overhead 20

DConstructor: Efficient and Robust Network Construction with...

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39th symposium on principles of distributed computing

作者： Gilbert, Seth Pandurangan, Gopal Robinson, Peter Trehan, Amitabh Natl Univ Singapore Dept Comp Sci Singapore Singapore Univ Houston Dept Comp Sci Houston TX 77004 USA City Univ Hong Kong Dept Comp Sci Hong Kong Peoples R China Loughborough Univ Dept Comp Sci Loughborough Leics England

ISBN: (纸本)9781450375825

With the rise of dynamic reconfigurable networks such as Peer-to-Peer (P2P) networks, overlay networks, ad hoc wireless and mesh networks, it has become important to construct and maintain topologies with various desirable properties (such as connectivity, low diameter, expansion, low degree etc.) in an efficient decentralized manner. The main result of this paper is a distributed protocol called DConstructor that given any (connected) network topology will "converge" to a given (desired) target topology such as an expander, hypercube, or Chord, with high probability. Our protocol is efficient, lightweight, and scalable, and it incurs only O (polylog(n)) overhead (where.. is the network size) for topology construction and maintenance: only polylogarithmic (in n) bits need to be processed and sent by each node per round, the convergence time is polylogarithmic rounds and any node's computation cost per round is also polylogarithmic. Our protocol is robust and self-repairing in the sense that it will converge to the desired topology in polylogarithmic rounds and polylogarithmic communication cost under dynamic topology changes and arbitrary insertions and deletions of nodes.

关键词： distributed Protocol Peer-to-Peer Network Randomized Algorithm Self-repairing Network Expander

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distributed Approximation on Power Graphs 20

Distributed Approximation on Power Graphs

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39th symposium on principles of distributed computing

作者： Bar-Yehuda, Reuven Censor-Hillel, Keren Maus, Yannic Pai, Shreyas Pemmaraju, Sriram V. Technion Israel Inst Technol Haifa Israel Univ Iowa Iowa City IA USA

ISBN: (纸本)9781450375825

We investigate graph problems in the following setting: we are given a graph G and we are required to solve a problem on G(2). While we focus mostly on exploring this theme in the distributed CONGEST model, we also show new results and surprising connections to the centralized model of computation. In the CONGEST model, it is natural to expect that problems on G(2) would be quite difficult to solve efficiently on G, due to congestion. However, we show that the picture is both more complicated and more interesting. Specifically, we encounter two phenomena acting in opposing directions: (i) slowdown due to congestion and (ii) speedup due to structural properties of G(2). We demonstrate these two phenomena via two fundamental graph problems, namely, Minimum Vertex Cover (MVC) and Minimum Dominating Set (MDS). Among our many contributions, the highlights are the following. (1) In the CONGEST model, we show an O(n/epsilon)-round (1 + epsilon)approximation algorithm for MVC on G(2), whereas no o(n(2))round algorithm is known for any better-than-2 approximation for MVC on G. (2) We show a centralized polynomial time 5/3-approximation algorithm for MVC on G(2), whereas a better-than-2 approximation is UGC-hard for G. (3) In contrast, for MDS, in the CONGEST model, we show an (Omega) over tilde (n(2)) lower bound for a constant approximation factor for MDS on G(2), whereas an (Omega) over tilde (n(2)) lower bound for MDS on G is known only for exact computation.

关键词： Approximation algorithms

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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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