We propose a family of constant-degree 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 peer-to-peer 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.

In this paper, we give a theoretical analysis of peer-to-peer (P2P) networks operating in the face of concurrent joins and unexpected departures. We focus on Chord, a recently developed P2P system that implements a distributed hash table abstraction, and study the process by which Chord maintains its distributed state as nodes join and leave the system. We argue that traditional performance measures based on run-time are uninformative for a continually running P2P network, and that the rate at which nodes in the network need to participate to maintain system state is a more useful metric. We give a general lower bound on this rate for a network to remain connected, and prove that an appropriately modified version of Chord's maintenance rate is within a logarithmic factor of the optimum rate. 1.

We propose a new approach for constructing P2P networks based on a dynamic decomposition of a continuous space into cells corresponding to processors. We demonstrate the power of these design rules by suggesting two new architectures, one for DHT (Distributed Hash Table) and the other for dynamic expander networks. The DHT network, which we call Distance Halving, allows logarithmic routing and load, while preserving constant degrees. Our second construction builds a network that is guaranteed to be an expander. The resulting topologies are simple to maintain and implement. Their simplicity makes it easy to modify and add protocols. We show it is possible to reduce the dilation and the load of the DHT with a small increase of the degree. We present a provably good protocol for relieving hot spots and a construction with high fault tolerance. Finally we show that, using our approach, it is possible to construct any family of constant degree graphs in a dynamic environment, though with worst parameters. Therefore we expect that more distributed data structures could be designed and implemented in a dynamic environment.

This paper examines graph-theoretic properties of existing peer-to-peer architectures and proposes a new infrastructure based on optimal-diameter 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 peer-to-peer 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 peer-to-peer networks. Having confirmed that de Bruijn graphs offer the best diameter and highest connectivity among the existing peer-to-peer 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 peer-to-peer architecture

The success of a P2P file-sharing network highly depends on the scalability and versatility of its search mechanism. Two particularly desirable search features are scope (ability to find infrequent items) and support for partial-match queries (queries that contain typos or include a subset of keywords). While centralized-index architectures (such as Napster) can support both these features, existing decentralized architectures seem to support at most one: prevailing unstructured P2P protocols (such as Gnutella and FastTrack) deploy a "blind" search mechanism where the set of peers probed is unrelated to the query; thus they support partial-match queries but have limited scope. On the other extreme, the recently-proposed distributed hash tables (DHTs) such as CAN and CHORD, couple index location with the item's hash value, and thus have good scope but can not effectively support partial-match queries. Another hurdle to DHTs deployment is their tight control of the overlay structure and the information (part of the index) each peer maintains, which makes them more sensitive to failures and frequent joins and disconnects.

We describe a content addressable network which is robust in the face of massive adversarial attacks and in a highly dynamic environment. Our network is robust in the sense that at any time, an arbitrarily large fraction of the peers can reach an arbitrarily large fraction of the data items. The network can be created and maintained in a completely distributed fashion.

A content-addressable network (CAN) is a distributed lookup table that can be used to implement peer-to-peer (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.

This paper presents a generic scheme for a central, yet untackled issue in overlay dynamic networks: maintaining stability over long life and against malicious adversaries. The generic scheme maintains desirable properties of the underlying structure including low diameter, and efficient routing mechanism, as well as balanced node dispersal. These desired properties are maintained in a decentralized manner without resorting to global updates or periodic stabilization protocols even against an adaptive adversary that controls the arrival and departure of nodes.

We introduce a distributed hash table (DHT) with logarithmic degree and logarithmic dilation. We show two lookup algorithms. The first has a message complexity of log n and is robust under random deletion of nodes. The second has parallel time of log n and message complexity of log^2 n. It is robust under spam induced by a random subset of the nodes. The construction has competitive parameters when compared to other DHT's. Its main merits are its simplicity, its flexibility and the fresh ideas introduced in its design. It is very easy to modify and to add more sophisticated protocols, such as dynamic caching and erasure correcting codes.

In this paper, we show that two peer-to-peer systems, Pastry [13] and Tapestry [17] can be made tolerant to certain classes of failures and a limited class of attacks. These systems are said to operate properly if they can find the closest node matching a requested ID.