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43
Skip Graphs
 Proc. of the 14th Annual ACMSIAM Symp. on Discrete Algorithms
, 2003
"... Skip graphs are a novel distributed data structure, based on skip lists, that provide the full functionality of a balanced tree in a distributed system where resources are stored in separate nodes that may fail at any time. They are designed for use in searching peertopeer systems, and by providin ..."
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Cited by 235 (9 self)
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Skip graphs are a novel distributed data structure, based on skip lists, that provide the full functionality of a balanced tree in a distributed system where resources are stored in separate nodes that may fail at any time. They are designed for use in searching peertopeer systems, and by providing the ability to perform queries based on key ordering, they improve on existing search tools that provide only hash table functionality. Unlike skip lists or other tree data structures, skip graphs are highly resilient, tolerating a large fraction of failed nodes without losing connectivity. In addition, constructing, inserting new nodes into, searching a skip graph, and detecting and repairing errors in the data structure introduced by node failures can be done using simple and straightforward algorithms. 1
GraphTheoretic Analysis of Structured PeertoPeer Systems: Routing Distances and Fault Resilience
, 2003
"... This paper examines graphtheoretic properties of existing peertopeer architectures and proposes a new infrastructure based on optimaldiameter de Bruijn graphs. Since generalized de Bruijn graphs possess very short average routing distances and high resilience to node failure, they are well suite ..."
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Cited by 105 (7 self)
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This paper examines graphtheoretic properties of existing peertopeer architectures and proposes a new infrastructure based on optimaldiameter de Bruijn graphs. Since generalized de Bruijn graphs possess very short average routing distances and high resilience to node failure, they are well suited for structured peertopeer networks. Using the example of Chord, CAN, and de Bruijn, we first study routing performance, graph expansion, and clustering properties of each graph. We then examine bisection width, path overlap, and several other properties that affect routing and resilience of peertopeer networks. Having confirmed that de Bruijn graphs offer the best diameter and highest connectivity among the existing peertopeer structures, we offer a very simple incremental building process that preserves optimal properties of de Bruijn graphs under uniform user joins/departures. We call the combined peertopeer architecture
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 89 (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 57 (6 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
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 45 (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.
A statistical theory of chord under churn
 In 4th International Workshop on PeerToPeer Systems
, 2005
"... Abstract. Most earlier studies of DHTs under churn have either depended on simulations as the primary investigation tool, or on establishing bounds for DHTs to function. In this paper, we present a complete analytical study of churn using a masterequationbased approach, used traditionally in noneq ..."
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Cited by 31 (1 self)
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Abstract. Most earlier studies of DHTs under churn have either depended on simulations as the primary investigation tool, or on establishing bounds for DHTs to function. In this paper, we present a complete analytical study of churn using a masterequationbased approach, used traditionally in nonequilibrium statistical mechanics to describe steadystate or transient phenomena. Simulations are used to verify all theoretical predictions. We demonstrate the application of our methodology to the Chord system. For any rate of churn and stabilization rates, and any system size, we accurately predict the fraction of failed or incorrect successor and finger pointers and show how we can use these quantities to predict the performance and consistency of lookups under churn. We also discuss briefly how churn may actually be of different ’types’ and the implications this will have for the functioning of DHTs in general. 1
Compact Routing on Euclidian Metrics
, 2004
"... We consider the problem of designing a compact communication network that supports e#cient routing in an Euclidean plane. Our network design and routing scheme achieves 1+# stretch, logarithmic diameter, and constant out degree. This improves upon the best known result so far that requires a logari ..."
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Cited by 29 (4 self)
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We consider the problem of designing a compact communication network that supports e#cient routing in an Euclidean plane. Our network design and routing scheme achieves 1+# stretch, logarithmic diameter, and constant out degree. This improves upon the best known result so far that requires a logarithmic outdegree. Furthermore, our scheme is asymptotically optimal in Euclidean metrics whose diameter is polynomial.
Know thy Neighbor's Neighbor: Better Routing for SkipGraphs and Small Worlds
 in Proc. of IPTPS, 2004
, 2004
"... We investigate an approach for routing in p2p networks called neighborofneighbor greedy. We show that this approach may reduce significantly the number of hops used, when routing in skip graphs and small worlds. Furthermore we show that a simple variation of Chord is degree optimal. Our algorithm ..."
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Cited by 20 (1 self)
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We investigate an approach for routing in p2p networks called neighborofneighbor greedy. We show that this approach may reduce significantly the number of hops used, when routing in skip graphs and small worlds. Furthermore we show that a simple variation of Chord is degree optimal. Our algorithm is implemented on top of the conventional greedy algorithms, thus it maintains the good properties of greedy routing. Implementing it may only improve the performance of the system.
Selfstabilizing structured ring topology p2p systems
"... We propose a selfstabilizing and modeless peertopeer(P2P) network construction and maintenance protocol, called the Ring Network(RN) protocol. The RN protocol, when started on a network of peers that are in an arbitrary state, will cause the network to converge to a structured P2P system with a di ..."
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Cited by 19 (0 self)
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We propose a selfstabilizing and modeless peertopeer(P2P) network construction and maintenance protocol, called the Ring Network(RN) protocol. The RN protocol, when started on a network of peers that are in an arbitrary state, will cause the network to converge to a structured P2P system with a directed ring topology, where peers are ordered according to their identifiers. Furthermore, the RN protocol maintains this structure in the face of peer joins and departures. The RN protocol is a distributed and asynchronous messagepassing protocol, which fits well the autonomous behavior of peers in a P2P system. The RN protocol requires only the existence of a bootstrapping system which is weakly connected. Peers do not need to be informed of any global network state, nor do they need to assist in repairing the network topology when they leave. We provide a proof of the selfstabilizing nature of the protocol, and experimentally measure the average cost (in time and number of messages) to achieve convergence. 1.
A doubling dimension threshold Θ(log log n) for augmented graph navigability
 In 14th European Symposium on Algorithm (ESA), LNCS 4168
, 2006
"... Abstract. In his seminal work, Kleinberg showed how to augment meshes using random edges, so that they become navigable; that is, greedy routing computes paths of polylogarithmic expected length between any pairs of nodes. This yields the crucial question of determining wether such an augmentation i ..."
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Cited by 17 (7 self)
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Abstract. In his seminal work, Kleinberg showed how to augment meshes using random edges, so that they become navigable; that is, greedy routing computes paths of polylogarithmic expected length between any pairs of nodes. This yields the crucial question of determining wether such an augmentation is possible for all graphs. In this paper, we answer negatively to this question by exhibiting a threshold on the doubling dimension, above which an infinite family of graphs cannot be augmented to become navigable whatever the distribution of random edges is. Precisely, it was known that graphs of doubling dimension at most O(log log n) are navigable. We show that for doubling dimension ≫ log log n, an infinite family of graphs cannot be augmented to become navigable. Finally, we complete our result by studying the special case of square meshes, that we prove to always be augmentable to become navigable.