How Efficient Can Gossip Be? (On the Cost of Resilient Information Exchange)

Alistarh, Dan; Gilbert, Seth; Guerraoui, Rachid; Zadimoghaddam, Morteza

doi:10.1007/978-3-642-14162-1_10

Cited by 13 publications

(23 citation statements)

References 31 publications

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“…The improvement relies on a key property of the DRR scheme that we prove: the height of each tree produced by DRR in any arbitrary graph is bounded by O(log n) w.h.p. 1 In Chord, for example, we show that DRR-gossip takes O(log 2 n) time w.h.p.…”

Section: Algorithmmentioning

confidence: 95%

Almost-Optimal Gossip-Based Aggregate Computation

Chen¹,

Pandurangan²

2012

SIAM J. Comput.

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Motivated by applications to modern networking technologies, there has been interest in designing efficient gossip-based protocols for computing aggregate functions. While gossip-based protocols provide robustness due to their randomized nature, reducing the message and time complexity of these protocols is also of paramount importance in the context of resource-constrained networks such as sensor and peer-to-peer networks. We present provably time-optimal efficient gossip-based algorithms for aggregate computation with almost optimal message complexity. Given an n-node network, our algorithms guarantee that all the nodes can compute the common aggregates (such as Max, Min, Average, Sum, and Count) of their values in optimal O(log n) time and using O(n log log n) messages. Our result improves on the algorithm of Kempe, Dobra, and Gehrke [Proceedings of the IEEE Annual Symposium on Foundations of Computer Science, 2003, pp. 482-491] that is timeoptimal but uses O(n log n) messages, as well as on the algorithm of Kashyap et al. [Proceedings of Symposium on Principles of Database Systems, 2006, pp. 308-317] that uses O(n log log n) messages but is not time-optimal (takes O(log n log log n) time). Furthermore, we show that our algorithms can be used to improve gossip-based aggregate computation in sparse communication networks, such as in peer-to-peer networks. The main technical ingredient of our algorithm is a technique called distributed random ranking (DRR) that can be useful in other applications as well. DRR gives an efficient distributed procedure to partition the network into a forest of (disjoint) trees of small size. Since the size of each tree is small, aggregates within each tree can be efficiently obtained at their respective roots. All the roots then perform a uniform gossip algorithm on their local aggregates to reach a distributed consensus on the global aggregates. Our algorithms are non-address-oblivious. In contrast, we show a lower bound of Ω(n log n) on the message complexity of any address-oblivious algorithm for computing aggregates. This shows that non-address-oblivious algorithms are needed to obtain significantly better message complexity. Our lower bound holds regardless of the number of rounds taken or the size of the messages used. Our lower bound is the first nontrivial lower bound for gossip-based aggregate computation and also gives the first formal proof that computing aggregates is strictly harder than rumor spreading in the address-oblivious model.

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Section: Algorithmmentioning

confidence: 95%

Almost-Optimal Gossip-Based Aggregate Computation

Chen¹,

Pandurangan²

2012

SIAM J. Comput.

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“…There is also much work on achieving data consistency through replication in message-passing systems (e.g., [4]). More recently, gossip protocols [20,27,28,17,2] have received considerable attention. In gossip (also called rumor-spreading), the goal is to quickly disseminate information throughout the network or compute some aggregate function of the information; this is achieved by having every node contact a small number of other nodes (typically, but not always, selected at random) to exchange information with them.…”

Section: Introductionmentioning

confidence: 99%

A Tight Bound for Set Disjointness in the Message-Passing Model

Braverman

Ellen

Oshman

et al. 2013

2013 IEEE 54th Annual Symposium on Foundations of Computer Science

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In a multiparty message-passing model of communication, there are k players. Each player has a private input, and they communicate by sending messages to one another over private channels. While this model has been used extensively in distributed computing and in multiparty computation, lower bounds on communication complexity in this model and related models have been somewhat scarce. In recent work [40,46,47], strong lower bounds of the form Ω(n · k) were obtained for several functions in the message-passing model; however, a lower bound on the classical Set Disjointness problem remained elusive.In this paper, we prove tight lower bounds of the form Ω(n · k) for the Set Disjointness problem in the message passing model. Our bounds are obtained by developing information complexity tools in the message-passing model, and then proving an information complexity lower bound for Set Disjointness. As a corollary, we show a tight lower bound for the task allocation problem [19] via a reduction from One of the most natural application domains for communication complexity is distributed computing: When we wish to study the cost of computing in a network spanning multiple cores or physical machines, it is very useful to understand how much communication is necessary, since communication between machines often dominates the cost of the computation. Accordingly, lower bounds in communication complexity have been used to obtain many negative results in distributed computing, from the round complexity of finding a minimum-weight spanning tree [42] to computing functions of distributed data [37,29] and distributed computation and verification of network graph structures and properties [42,23].To the best of our knowledge, however, all applications of communication complexity lower bounds in distributed computing to date have used only two-player lower bounds. The reason for this appears to be twofold: First, the models of multi-party communication favored by the communication complexity community, the number-on-forehead model and the number-in-hand broadcast model, do not correspond to most natural models of distributed computing. Second, two-party lower bounds are surprisingly powerful, even for networks with many players. A typical reduction from a two-player communication complexity problem to a distributed problem T finds a sparse cut in the network, and shows that, to solve T , the two sides of the cut must implicitly solve, say, Set Disjointness [30]. However, there are problems that cannot be addressed by reduction from a two-player problem, because such reductions must reveal almost the entire structure of the network to one of the two players. (One such example is described in [29].)In this paper, we study communication complexity in message-passing models, where each party has a private input, and the parties communicate by sending messages to each other over private channels. These models have been used extensively in distributed computing, for example, to study gossiping protocols [27], to compute various functions...

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“…For instance, [37], [38] provide such complexity bounds on gossiping, broadcast, and rumor spreading in such networks. Also, influential works by Peleg et al in the spirit of [39] demonstrate important complexity lower bounds on broadcast in radius-2 radio networks: the broadcast procedure requires V(log 2 n) transmissions.…”

Section: Related Workmentioning

confidence: 98%

Towards Optimal Broadcast in Wireless Networks

Nikolov

Haas

2015

IEEE Trans. on Mobile Comput.

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Broadcast is a fundamental operation in networks, especially in reconfigurable wireless ad hoc networks. For example, some form of broadcasting is used by all on-demand mobile networks routing protocols, when there is uncertainty as to the location of the destination node, or for service discovery. In this work, we present a new approach to efficient broadcast in networks with dynamic topologies, and we introduce the time sequence scheme (TSS), a new online local broadcasting algorithm for such networking environments. TSS ranks by priority, in a distributed way, candidate broadcasting nodes so that the overall number of re-broadcasts in the network is minimized. We evaluate TSS, showing that its performance comes remarkably close to the corresponding theoretical performance bounds, even in the presence of packet loss due, for example, to MAC-layer collisions. Furthermore, we compare our algorithm with a number of recently proposed schemes considering their performance in various realistic network mobility scenarios. We demonstrate that TSS performance is robust in the context of mobility induced topology reconfigurations-including temporal network partitioning-during propagation of the broadcast message.

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How Efficient Can Gossip Be? (On the Cost of Resilient Information Exchange)

Cited by 13 publications

References 31 publications

Almost-Optimal Gossip-Based Aggregate Computation

Almost-Optimal Gossip-Based Aggregate Computation

A Tight Bound for Set Disjointness in the Message-Passing Model

Towards Optimal Broadcast in Wireless Networks

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