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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 ..."
Abstract

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.
EdgeDisjoint Paths in Expander Graphs
, 2000
"... Given a graph G = (V, E) and a set of n pairs of vertices in V, we are interested in finding for each pair (ai, bi), a path connecting ai to bi, such that the set of n paths so found is edgedisjoint. (For arbitrary graphs the problem is AfPcomplete, although it is in 7 > if n is fixed.) We pre ..."
Abstract

Cited by 19 (0 self)
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Given a graph G = (V, E) and a set of n pairs of vertices in V, we are interested in finding for each pair (ai, bi), a path connecting ai to bi, such that the set of n paths so found is edgedisjoint. (For arbitrary graphs the problem is AfPcomplete, although it is in 7 > if n is fixed.) We present a polynomial time randomized algorithm for finding edge disjoint paths in an rregular expander graph G. We show that if G has sufficiently strong expansion properties and r is sufficiently large then all sets of n = f(n/log n) pairs of vertices can be joined. This is within a constant factor of best possible.
Finding disjoint paths in expanders deterministically and online
, 2007
"... We describe a deterministic, polynomial time algorithm for finding edgedisjoint paths connecting given pairs of vertices in an expander. Specifically, the input of the algorithm is a sufficiently strong dregular expander G on n vertices, and a sequence of pairs si, ti, (1 ≤ i ≤ r) of vertices, whe ..."
Abstract

Cited by 3 (0 self)
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We describe a deterministic, polynomial time algorithm for finding edgedisjoint paths connecting given pairs of vertices in an expander. Specifically, the input of the algorithm is a sufficiently strong dregular expander G on n vertices, and a sequence of pairs si, ti, (1 ≤ i ≤ r) of vertices, where r = Θ( nd log d log n), and no vertex appears more than d/3 times in the list of all endpoints s1, t1,..., sr, tr. The algorithm outputs edgedisjoint paths Q1,..., Qr, where Qi connects si and ti. The paths are constructed online, that is, the algorithm produces Qi as soon as it gets si, ti and before the next requests in the sequence are revealed. This improves in several respects a long list of previous algorithms for the above problem, whose study is motivated by the investigation of communication networks. An analogous result is established for vertex disjoint paths in blowups of strong expanders. 1