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20
Bimodal Multicast
 ACM Transactions on Computer Systems
, 1998
"... This paper looks at reliability with a new goal: development of a multicast protocol which is reliable in a sense that can be rigorously quantified and includes throughput stability guarantees. We characterize this new protocol as a "bimodal multicast" in reference to its reliability model, which co ..."
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Cited by 192 (11 self)
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This paper looks at reliability with a new goal: development of a multicast protocol which is reliable in a sense that can be rigorously quantified and includes throughput stability guarantees. We characterize this new protocol as a "bimodal multicast" in reference to its reliability model, which corresponds to a family of bimodal probability distributions. Here, we introduce the protocol, provide a theoretical analysis of its behavior, review experimental results, and discuss some candidate applications. These confirm that bimodal multicast is reliable, scalable, and that the protocol provides remarkably stable delivery throughput
Protocols and impossibility results for gossipbased communication mechanisms
, 2002
"... In recent years, gossipbased algorithms have gained prominence as a methodology for designing robust and scalable communication schemes in large distributed systems. The premise underlying distributed gossip is very simple: in each time step, each node v in the system selects some other node w as a ..."
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Cited by 55 (3 self)
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In recent years, gossipbased algorithms have gained prominence as a methodology for designing robust and scalable communication schemes in large distributed systems. The premise underlying distributed gossip is very simple: in each time step, each node v in the system selects some other node w as a communication partner — generally by a simple randomized rule — and exchanges information with w; over a period of time, information spreads through the system in an “epidemic fashion”. A fundamental issue which is not well understood is the following: how does the underlying lowlevel gossip mechanism — the means by which communication partners are chosen — affect one’s ability to design efficient highlevel gossipbased protocols? We establish one of the first concrete results addressing this question, by showing a fundamental limitation on the power of the commonly used uniform gossip mechanism for solving nearestresource location problems. In contrast, very efficient protocols for this problem can be designed using a nonuniform spatial gossip mechanism, as established in earlier work with Alan Demers. We go on to consider the design of protocols for more complex problems, providing an efficient distributed gossipbased protocol for a set of nodes in Euclidean space to construct an approximate minimum spanning tree. Here too, we establish a contrasting limitation on the power of uniform gossip for solving this problem. Finally, we investigate gossipbased packet routing as a primitive that underpins the communication patterns in many protocols, and as a way to understand the capabilities of different gossip mechanisms at a general level.
Quasirandom Rumor Spreading
 In Proc. of SODA’08
, 2008
"... We propose and analyse a quasirandom analogue to the classical push model for disseminating information in networks (“randomized rumor spreading”). In the classical model, in each round each informed node chooses a neighbor at random and informs it. Results of Frieze and Grimmett (Discrete Appl. Mat ..."
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Cited by 24 (10 self)
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We propose and analyse a quasirandom analogue to the classical push model for disseminating information in networks (“randomized rumor spreading”). In the classical model, in each round each informed node chooses a neighbor at random and informs it. Results of Frieze and Grimmett (Discrete Appl. Math. 1985) show that this simple protocol succeeds in spreading a rumor from one node of a complete graph to all others within O(log n) rounds. For the network being a hypercube or a random graph G(n, p) with p ≥ (1+ε)(log n)/n, also O(log n) rounds suffice (Feige, Peleg, Raghavan, and Upfal, Random Struct. Algorithms 1990). In the quasirandom model, we assume that each node has a (cyclic) list of its neighbors. Once informed, it starts at a random position of the list, but from then on informs its neighbors in the order of the list. Surprisingly, irrespective of the orders of the lists, the above mentioned bounds still hold. In addition, we also show a O(log n) bound for sparsely connected random graphs G(n, p) with p = (log n+f(n))/n, where f(n) → ∞ and f(n) = O(log log n). Here, the classical model needs Θ(log 2 (n)) rounds. Hence the quasirandom model achieves similar or better broadcasting times with a greatly reduced use of random bits.
Rumour spreading and graph conductance
 IN PROCEEDINGS OF THE 21ST ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS (SODA
, 2010
"... We show that if a connected graph with n nodes has conductance φ then rumour spreading, also known as randomized broadcast, successfully broadcasts a message within O(log 4 n/φ 6) many steps, with high probability, using the PUSHPULL strategy. An interesting feature of our approach is that it draws ..."
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Cited by 21 (2 self)
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We show that if a connected graph with n nodes has conductance φ then rumour spreading, also known as randomized broadcast, successfully broadcasts a message within O(log 4 n/φ 6) many steps, with high probability, using the PUSHPULL strategy. An interesting feature of our approach is that it draws a connection between rumour spreading and the spectral sparsification procedure of Spielman and Teng [23].
On the runtime and robustness of randomized broadcasting
 In Proc. of ISAAC’ 06
, 2006
"... Abstract. One of the most frequently studied problems in the context of information dissemination in communication networks is the broadcasting problem. In this paper, we study the following randomized broadcasting protocol. At some time t an information r is placed at one of the nodes of a graph. I ..."
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Cited by 15 (5 self)
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Abstract. One of the most frequently studied problems in the context of information dissemination in communication networks is the broadcasting problem. In this paper, we study the following randomized broadcasting protocol. At some time t an information r is placed at one of the nodes of a graph. In the succeeding steps, each informed node chooses one neighbor, independently and uniformly at random, and informs this neighbor by sending a copy of r to it. In this work, we develop tight bounds on the runtime of the algorithm described above, and analyze its robustness. First, it is shown that on Δregular graphs this algorithm requires at least log2 − 1 N +log Δ
Nearperfect load balancing by randomized rounding
 In 41st Annual ACM Symposium on Theory of Computing (STOC’09
, 2009
"... We consider and analyze a new algorithm for balancing indivisible loads on a distributed network with n processors. The aim is minimizing the discrepancy between the maximum and minimum load. In every timestep paired processors balance their load as evenly as possible. The direction of the excess t ..."
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Cited by 14 (10 self)
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We consider and analyze a new algorithm for balancing indivisible loads on a distributed network with n processors. The aim is minimizing the discrepancy between the maximum and minimum load. In every timestep paired processors balance their load as evenly as possible. The direction of the excess token is chosen according to a randomized rounding of the participating loads. We prove that in comparison to the corresponding model of Rabani, Sinclair, and Wanka (1998) with arbitrary roundings, the randomization yields an improvement of roughly a square root of the achieved discrepancy in the same number of timesteps on all graphs. For the important case of expanders we can even achieve a constant discrepancy in O(log n(log log n) 3) rounds. This is optimal up to log log nfactors while the best previous algorithms in this setting either require Ω(log 2 n) time or can only achieve a logarithmic discrepancy. This result also demonstrates that with randomized rounding the difference between discrete and continuous load balancing vanishes almost completely.
Parsimonious flooding in dynamic graphs
 In Proc. of 28th Symp. on Principles of Distributed Computing (PODC
, 2009
"... An edgeMarkovian process with birthrate p and deathrate q generates sequences of graphs (G0, G1, G2,...) with the same node set [n] such that Gt is obtained from Gt−1 as follows: if e / ∈ E(Gt−1) then e ∈ E(Gt) with probability p, and if e ∈ E(Gt−1) then e / ∈ E(Gt) with probability q. Clementi e ..."
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Cited by 14 (1 self)
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An edgeMarkovian process with birthrate p and deathrate q generates sequences of graphs (G0, G1, G2,...) with the same node set [n] such that Gt is obtained from Gt−1 as follows: if e / ∈ E(Gt−1) then e ∈ E(Gt) with probability p, and if e ∈ E(Gt−1) then e / ∈ E(Gt) with probability q. Clementi et al. (PODC 2008) analyzed thoroughly information dissemination in such dynamic graphs, by establishing bounds on their flooding time — flooding is the basic mechanism in which every node becoming aware of an information at step t forwards this information to all its neighbors at all forthcoming steps t ′> t. In this paper, we establish tight bounds on the complexity of flooding for all possible birth rates and death rates, completing the previous results by Clementi et al. Moreover, we note that despite its many advantages in term of simplicity and robustness, flooding suffers from its high bandwidth consumption. Hence we al! so show that flooding in dynamic graphs can be implemented in a more parsimonious manner, so that to save bandwidth, yet preserving efficiency in term of simplicity and completion time. For a positive integer k, we say that the flooding protocol is kactive if each node forwards an information only during the k time steps immediately following the step at which the node receives that information for the first time. We define the reachability threshold for the flooding protocol as the smallest integer k such that, for any source s ∈ [n], the kactive flooding protocol from s completes (i.e., reaches all nodes), and we establish tight bounds for this parameter. We show that, for a large spectrum of parameters p and q, the reachability threshold is by several orders of magnitude smaller than the flooding time. In particular, we show A part of this work was done during the stay of the second
Formal Analysis Techniques for Gossiping Protocols
 ACM SIGOPS Oper. Syst. Rev.
, 2007
"... We give a survey of formal verification techniques that can be used to corroborate existing experimental results for gossiping protocols in a rigorous manner. We present properties of interest for gossiping protocols and discuss how various formal evaluation techniques can be employed to predict the ..."
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Cited by 11 (4 self)
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We give a survey of formal verification techniques that can be used to corroborate existing experimental results for gossiping protocols in a rigorous manner. We present properties of interest for gossiping protocols and discuss how various formal evaluation techniques can be employed to predict them.
Fast Information Spreading in Graphs with Large Weak Conductance
"... Gathering data from nodes in a network is at the heart of many distributed applications, most notably, while performing a global task. We consider information spreading among n nodes of a network, where each node v has a message m(v) which must be received by all other nodes. The time required for i ..."
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Cited by 8 (1 self)
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Gathering data from nodes in a network is at the heart of many distributed applications, most notably, while performing a global task. We consider information spreading among n nodes of a network, where each node v has a message m(v) which must be received by all other nodes. The time required for information spreading has been previously upperbounded with an inverse relationship to the conductance of the underlying communication graph. This implies high running times for graphs with small conductance. The main contribution of this paper is an information spreading algorithm which overcomes communication bottlenecks and thus achieves fast information spreading for a wide class of graphs, despite their small conductance. As a key tool in our study we use the recently defined concept of
Approximation Algorithms for Structured Communication Problems
 In 9th ACM Symposium on Parallel Algorithms and Architectures (SPAA '97
, 1997
"... Given a network of processors, a structured communication problem consists to route a communication pattern known in advance. Structured communication problems appear frequently in parallel computing. Hence, communication libraries (e.g, PVM or MPI) generally include a specific access to procedures ..."
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Cited by 6 (4 self)
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Given a network of processors, a structured communication problem consists to route a communication pattern known in advance. Structured communication problems appear frequently in parallel computing. Hence, communication libraries (e.g, PVM or MPI) generally include a specific access to procedures solving the most common problems of this type. A standard communication model assumes that information proceeds by a sequence of calls between neighboring nodes of the network, and that each node is allowed to call at most one neighbor at a time. In this context, most of the decision problems corresponding to the usual structured communication problems have been shown to be NPcomplete. Therefore, several approximation algorithms have been proposed to solve specific problems. Each of these algorithms is dedicated to a particular problem. In this paper, we present a high level method which can be used to derive approximation algorithms for many different structured communication problems on ...