A fundamental problem that confronts peer-to-peer applications is to efficiently locate the node that stores a particular data item. This paper presents Chord, a distributed lookup protocol that addresses this problem. Chord provides support for just one operation: given a key, it maps the key onto a node. Data location can be easily implemented on top of Chord by associating a key with each data item, and storing the key/data item pair at the node to which the key maps. Chord adapts efficiently as nodes join and leave the system, and can answer queries even if the system is continuously changing. Results from theoretical analysis, simulations, and experiments show that Chord is scalable, with communication cost and the state maintained by each node scaling logarithmically with the number of Chord nodes.

Chord: A scalable peer-to-peer lookup service for internet applications

This paper presents the design and evaluation of Pastry, a scalable, distributed object location and routing substrate for wide-area peer-to-peer ap- plications. Pastry performs application-level routing and object location in a po- tentially very large overlay network of nodes connected via the Internet. It can be used to support a variety of peer-to-peer applications, including global data storage, data sharing, group communication and naming. Each node in the Pastry network has a unique identifier (nodeId). When presented with a message and a key, a Pastry node efficiently routes the message to the node with a nodeId that is numerically closest to the key, among all currently live Pastry nodes. Each Pastry node keeps track of its immediate neighbors in the nodeId space, and notifies applications of new node arrivals, node failures and recoveries. Pastry takes into account network locality; it seeks to minimize the distance messages travel, according to a to scalar proximity metric like the number of IP routing hops. Pastry is completely decentralized, scalable, and self-organizing; it automatically adapts to the arrival, departure and failure of nodes. Experimental results obtained with a prototype implementation on an emulated network of up to 100,000 nodes confirm Pastry's scalability and efficiency, its ability to self-organize and adapt to node failures, and its good network locality properties.

/pdf/pastry-scalable-decentralized-object-location-and-routing-1u2equbbbp.pdf

Pastry: Scalable, Decentralized Object Location, and Routing for Large-Scale Peer-to-Peer Systems

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Hash tables - which map "keys" onto "values" - are an essential building block in modern software systems. We believe a similar functionality would be equally valuable to large distributed systems. In this paper, we introduce the concept of a Content-Addressable Network (CAN) as a distributed infrastructure that provides hash table-like functionality on Internet-like scales. The CAN is scalable, fault-tolerant and completely self-organizing, and we demonstrate its scalability, robustness and low-latency properties through simulation.

https://www.cs.sjtu.edu.cn/~gchen/course/acn/Reading/CAN.pdf

A scalable content-addressable network

Covering the basic techniques used in the latest research work, the author consolidates progress made so far, including some very recent and promising results, and conveys the beauty and excitement of work in the field. He gives clear, lucid explanations of key results and ideas, with intuitive proofs, and provides critical examples and numerous illustrations to help elucidate the algorithms. Many of the results presented have been simplified and new insights provided. Of interest to theoretical computer scientists, operations researchers, and discrete mathematicians.

Approximation Algorithms

Solitons and instantons

Consider a set of shared objects in a distributed network, where several copies of each object may exist at any given time. To ensure both fast access to the objects as well as efficient utilization of network resources, it is desirable that each access request be satisfied by a copy "close" to the requesting node. Unfortunately, it is not clear how to efficiently achieve this goal in a dynamic, distributed environment in which large numbers of objects are continuously being created, replicated, and destroyed. In this paper, we design a simple randomized algorithm for accessing shared objects that tends to satisfy each access request with a nearby copy. The algorithm is based on a novel mechanism to maintain and distribute information about object locations, and requires only a small amount of additional memory at each node. We analyze our access scheme for a class of cost functions that captures the hierarchical nature of wide-area networks. We show that under the particular cost model considered: (i) the expected cost of an individual access is asymptotically optimal, and (ii) if objects are sufficiently large, the memory used for objects dominates the additional memory used by our algorithm with high probability. We also address dynamic changes in both the network as well as the set of object copies.

Accessing nearby copies of replicated objects in a distributed environment

1. Preface cum introduction. 2. Classical solitons and solitary waves. 3. Monopoles and such. 4. Classical instanton solutions. 5. Quantisation of static solutions. 6. Functional integrals and the WKB method. 7. Some exact results. 8. Collective coordinates and canonical methods. 9. Semiclassical methods for Fermi fields. 10. Instantons in quantum theory. 11. Some more instanton effects. Appendices. References. Index.

Solitons and Instantons: An Introduction to Solitons and Instantons in Quantum Field Theory

Consider a set of shared objects in a distributed network, where several copies of each object may exist at any given time. To ensure both fast access to the objects as well as efficient utilization of network resources, it is desirable that each access request be satisfied by a copy ``close'' to the requesting node. Unfortunately, it is not clear how to achieve this goal efficiently in a dynamic, distributed environment in which large numbers of objects are continuously being created, replicated, and destroyed. In this paper we design a simple randomized algorithm for accessing shared objects that tends to satisfy each access request with a nearby copy. The algorithm is based on a novel mechanism to maintain and distribute information about object locations, and requires only a small amount of additional memory at each node. We analyze our access scheme for a class of cost functions that captures the hierarchical nature of wide-area networks. We show that under the particular cost model considered (i) the expected cost of an individual access is asymptotically optimal, and (ii) if objects are sufficiently large, the memory used for objects dominates the additional memory used by our algorithm with high probability. We also address dynamic changes in both the network and the set of object copies.

Accessing Nearby Copies of Replicated Objects in a Distributed Environment

An ad hoc wireless network, or simply an ad hoc network, consists of a collection of geographically distributed nodes that communicate with one other over a wireless medium. An ad hoc network differs from cellular networks in that there is no wired infrastructure and the communication capabilities of the network are limited by the battery power of the network nodes. One of the original motivations for ad hoc networks is found in military applications. A classic example of ad hoc networking is network of war fighters and their mobile platforms in battlefields. Indeed, a wealth of early research in the area involved the development of packet-radio networks (PRNs) and survivable radio networks [16]. While military applications still dominate the research needs in ad hoc networking, the recent rapid advent of mobile telephony and plethora of personal digital assistants has brought to the fore a number of potential commercial applications of ad hoc networks. Examples are disaster relief, conferencing, home networking, sensor networks, personal area networks, and embedded computing applications [37].The lack of a fixed infrastructure in ad hoc networks implies that any computation on the network needs to be carried out in a decentralized manner. Thus, many of the important problems in ad hoc networking can be formulated as problems in distributed computing. However, there are certain characteristics of ad hoc networks that makes this study somewhat different than traditional work in distributed computing. In this article, we review some of the characteristic features of ad hoc networks, formulate problems and survey research work done in the area. We focus on two basic problem domains: topology control, the problem of computing and maintaining a connected topology among the network nodes, and routing. This article is not intended to be a comprehensive survey on ad hoc networking. The choice of the problems discussed in this article are somewhat biased by the research interests of the author.The remainder of this article is organized as follows. In Section 2, we describe various aspects relevant to modeling ad hoc networks. In Section 3, we discuss topology control. Since the nodes of an ad hoc network are often associated with points in 2-dimensional space, topology control is closely tied to computational geometry; we will briefly review this relationship and extant work in the area. In Section 4, we discuss routing protocols for ad hoc networks. After a brief overview of the many protocols that have been proposed, we discuss alternative approaches based on the adversarial network model.

Rajmohan Rajaraman

Papers

Solitons and instantons

Accessing nearby copies of replicated objects in a distributed environment

Solitons and Instantons: An Introduction to Solitons and Instantons in Quantum Field Theory

Accessing Nearby Copies of Replicated Objects in a Distributed Environment

Topology control and routing in ad hoc networks: a survey