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86
Viceroy: A Scalable and Dynamic Emulation of the Butterfly
, 2002
"... We propose a family of constantdegree routing networks of logarithmic diameter, with the additional property that the addition or removal of a node to the network requires no global coordination, only a constant number of linkage changes in expectation, and a logarithmic number with high probabilit ..."
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Cited by 352 (16 self)
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We propose a family of constantdegree routing networks of logarithmic diameter, with the additional property that the addition or removal of a node to the network requires no global coordination, only a constant number of linkage changes in expectation, and a logarithmic number with high probability. Our randomized construction improves upon existing solutions, such as balanced search trees, by ensuring that the congestion of the network is always within a logarithmic factor of the optimum with high probability. Our construction derives from recent advances in the study of peertopeer lookup networks, where rapid changes require e#cient and distributed maintenance, and where the lookup e#ciency is impacted both by the lengths of paths to requested data and the presence or elimination of bottlenecks in the network.
A Survey and Comparison of PeertoPeer Overlay Network Schemes
 IEEE Communications Surveys and Tutorials
, 2005
"... Abstract — Over the Internet today, computing and communications environments are significantly more complex and chaotic than classical distributed systems, lacking any centralized organization or hierarchical control. There has been much interest in emerging PeertoPeer (P2P) network overlays beca ..."
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Cited by 293 (1 self)
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Abstract — Over the Internet today, computing and communications environments are significantly more complex and chaotic than classical distributed systems, lacking any centralized organization or hierarchical control. There has been much interest in emerging PeertoPeer (P2P) network overlays because they provide a good substrate for creating largescale data sharing, content distribution and applicationlevel multicast applications. These P2P networks try to provide a long list of features such as: selection of nearby peers, redundant storage, efficient search/location of data items, data permanence or guarantees, hierarchical naming, trust and authentication, and, anonymity. P2P networks potentially offer an efficient routing architecture that is selforganizing, massively scalable, and robust in the widearea, combining fault tolerance, load balancing and explicit notion of locality. In this paper, we present a survey and comparison of various Structured and Unstructured P2P networks. We categorize the various schemes into these two groups in the design spectrum and discuss the applicationlevel network performance of each group.
Geographic routing in social networks
, 2005
"... We live in a “small world,” where two arbitrary people are likely connected by a short chain of intermediate friends. With scant information about a target individual, people can successively forward a message along such a chain. Experimental studies have verified this property in real social networ ..."
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Cited by 231 (11 self)
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We live in a “small world,” where two arbitrary people are likely connected by a short chain of intermediate friends. With scant information about a target individual, people can successively forward a message along such a chain. Experimental studies have verified this property in real social networks, and theoretical models have been advanced to explain it. However, existing theoretical models have not been shown to capture behavior in realworld social networks. Here we introduce a richer model relating geography and socialnetwork friendship, in which the probability of befriending a particular person is inversely proportional to the number of closer people. In a large social network, we show that one third of the friendships are independent of geography, and the remainder exhibit the proposed relationship. Further, we prove analytically that short chains can be discovered in every network exhibiting the relationship.
Symphony: Distributed Hashing in a Small World
 IN PROCEEDINGS OF THE 4TH USENIX SYMPOSIUM ON INTERNET TECHNOLOGIES AND SYSTEMS
, 2003
"... We present Symphony, a novel protocol for maintaining distributed hash tables in a wide area network. The key idea is to arrange all participants along a ring and equip them with long distance contacts drawn from a family of harmonic distributions. Through simulation, we demonstrate that our constr ..."
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Cited by 215 (13 self)
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We present Symphony, a novel protocol for maintaining distributed hash tables in a wide area network. The key idea is to arrange all participants along a ring and equip them with long distance contacts drawn from a family of harmonic distributions. Through simulation, we demonstrate that our construction is scalable, flexible, stable in the presence of frequent updates and offers small average latency with only a handful of long distance links per node. The cost of updates when hosts join and leave is small.
Complex Networks and Decentralized Search Algorithms
 In Proceedings of the International Congress of Mathematicians (ICM
, 2006
"... The study of complex networks has emerged over the past several years as a theme spanning many disciplines, ranging from mathematics and computer science to the social and biological sciences. A significant amount of recent work in this area has focused on the development of random graph models that ..."
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Cited by 115 (1 self)
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The study of complex networks has emerged over the past several years as a theme spanning many disciplines, ranging from mathematics and computer science to the social and biological sciences. A significant amount of recent work in this area has focused on the development of random graph models that capture some of the qualitative properties observed in largescale network data; such models have the potential to help us reason, at a general level, about the ways in which realworld networks are organized. We survey one particular line of network research, concerned with smallworld phenomena and decentralized search algorithms, that illustrates this style of analysis. We begin by describing a wellknown experiment that provided the first empirical basis for the "six degrees of separation" phenomenon in social networks; we then discuss some probabilistic network models motivated by this work, illustrating how these models lead to novel algorithmic and graphtheoretic questions, and how they are supported by recent empirical studies of large social networks.
Know thy Neighbor's Neighbor: the Power of Lookahead in Randomized P2P Networks
 In Proceedings of the 36th ACM Symposium on Theory of Computing (STOC
, 2004
"... Several peertopeer networks are based upon randomized graph topologies that permit e#cient greedy routing, e.g., randomized hypercubes, randomized Chord, skipgraphs and constructions based upon smallworld percolation networks. In each of these networks, a node has outdegree #(log n), where n de ..."
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Cited by 104 (5 self)
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Several peertopeer networks are based upon randomized graph topologies that permit e#cient greedy routing, e.g., randomized hypercubes, randomized Chord, skipgraphs and constructions based upon smallworld percolation networks. In each of these networks, a node has outdegree #(log n), where n denotes the total number of nodes, and greedy routing is known to take O(log n) hops on average. We establish lowerbounds for greedy routing for these networks, and analyze NeighborofNeighbor (NoN)greedy routing. The idea behind NoN, as the name suggests, is to take a neighbor's neighbors into account for making better routing decisions.
Analyzing Kleinberg’s (and other) smallworld models
 in Proc. of ACM Symp. on Princ. of Dist. Comp. (PODC
, 2004
"... We analyze the properties of SmallWorld networks, where links are much more likely to connect “neighbor nodes ” than distant nodes. In particular, our analysis provides new results for Kleinberg’s SmallWorld model and its extensions. Kleinberg adds a number of directed longrange random links to a ..."
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Cited by 73 (8 self)
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We analyze the properties of SmallWorld networks, where links are much more likely to connect “neighbor nodes ” than distant nodes. In particular, our analysis provides new results for Kleinberg’s SmallWorld model and its extensions. Kleinberg adds a number of directed longrange random links to an n × n lattice network (vertices as nodes of a grid, undirected edges between any two adjacent nodes). Links have a nonuniform distribution that favors arcs to close nodes over more distant ones. He shows that the following phenomenon occurs: between any two nodes a path with expected length O(log 2 n) can be found using a simple greedy algorithm which has no global knowledge of longrange links. We show that Kleinberg’s analysis is tight: his algorithm achieves θ(log 2 n) delivery time. Moreover, we show that the expected diameter of the graph is θ(log n), a log n factor
The ContentAddressable Network D2B
, 2003
"... A contentaddressable network (CAN) is a distributed lookup table that can be used to implement peertopeer (P2P) systems. A CAN allows the discovery and location of data and/or resources, identi ed by keys, in a distributed network (e.g., Internet), in absence of centralized server or any hier ..."
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Cited by 57 (2 self)
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A contentaddressable network (CAN) is a distributed lookup table that can be used to implement peertopeer (P2P) systems. A CAN allows the discovery and location of data and/or resources, identi ed by keys, in a distributed network (e.g., Internet), in absence of centralized server or any hierarchical organization. Several networks have been recently described in the literature, and some of them have led to the development of experimental systems. We present a new CAN, called d2b. Its main characteristics are: simplicity, provability, and scalability. d2b allows the number of nodes n to vary between 1 and jKj where K is the set of keys managed by the network. In term of performances, any join or leave of a user implies a constant expected number of link modi cations, and, with high probability (w.h.p.), at most O(log n) link modi cations.
Routing Networks for Distributed Hash Tables
, 2003
"... Routing topologies for distributed hashing in peertopeer networks are classified into two categories: deterministic and randomized. A general technique for constructing deterministic routing topologies is presented. Using this technique, classical parallel interconnection networks can be adapted ..."
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Cited by 57 (7 self)
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Routing topologies for distributed hashing in peertopeer networks are classified into two categories: deterministic and randomized. A general technique for constructing deterministic routing topologies is presented. Using this technique, classical parallel interconnection networks can be adapted to handle the dynamic nature of participants in peertopeer networks. A unified picture of randomized routing topologies is also presented. Two new protocols are described which improve average latency as a function of outdegree. One of the protocols can be shown to be optimal with high probability. Finally, routing networks for distributed hashing are revisited from a systems perspective and several open design problems are listed.
Estimating Network Size from Local Information
 Information Processing Letters
, 2003
"... this paper, we provide a localized estimation scheme that has good worst case accuracy. The scheme requires each joining node to communicate only with two nodes, its initial contact and one additional node. The expected accuracy of our estimator is within the range n=2::n , provided that the join ..."
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Cited by 49 (1 self)
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this paper, we provide a localized estimation scheme that has good worst case accuracy. The scheme requires each joining node to communicate only with two nodes, its initial contact and one additional node. The expected accuracy of our estimator is within the range n=2::n , provided that the joiners' contact points are assigned at random