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

Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc. of the 6th SIAM Conference on Parallel Processing for Scientific Computing, 1993, 445--452; Hendrickson and Leland, A Multilevel Algorithm for Partitioning Graphs, Tech. report SAND 93-1301, Sandia National Laboratories, Albuquerque, NM, 1993]. From the early work it was clear that multilevel techniques held great promise; however, it was not known if they can be made to consistently produce high quality partitions for graphs arising in a wide range of application domains. We investigate the effectiveness of many different choices for all three phases: coarsening, partition of the coarsest graph, and refinement. In particular, we present a new coarsening heuristic (called heavy-edge heuristic) for which the size of the partition of the coarse graph is within a small factor of the size of the final partition obtained after multilevel refinement. We also present a much faster variation of the Kernighan--Lin (KL) algorithm for refining during uncoarsening. We test our scheme on a large number of graphs arising in various domains including finite element methods, linear programming, VLSI, and transportation. Our experiments show that our scheme produces partitions that are consistently better than those produced by spectral partitioning schemes in substantially smaller time. Also, when our scheme is used to compute fill-reducing orderings for sparse matrices, it produces orderings that have substantially smaller fill than the widely used multiple minimum degree algorithm.

/pdf/a-fast-and-high-quality-multilevel-scheme-for-partitioning-2i240yved4.pdf

A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs

Reliability at massive scale is one of the biggest challenges we face at Amazon.com, one of the largest e-commerce operations in the world; even the slightest outage has significant financial consequences and impacts customer trust. The Amazon.com platform, which provides services for many web sites worldwide, is implemented on top of an infrastructure of tens of thousands of servers and network components located in many datacenters around the world. At this scale, small and large components fail continuously and the way persistent state is managed in the face of these failures drives the reliability and scalability of the software systems.This paper presents the design and implementation of Dynamo, a highly available key-value storage system that some of Amazon's core services use to provide an "always-on" experience. To achieve this level of availability, Dynamo sacrifices consistency under certain failure scenarios. It makes extensive use of object versioning and application-assisted conflict resolution in a manner that provides a novel interface for developers to use.

/pdf/dynamo-amazon-s-highly-available-key-value-store-2ozfk43ou4.pdf

Dynamo: amazon's highly available key-value store

Computational geometry is concerned with the design and analysis of algorithms for geometrical problems. In addition, other more practically oriented, areas of computer science— such as computer graphics, computer-aided design, robotics, pattern recognition, and operations research—give rise to problems that inherently are geometrical. This is one reason computational geometry has attracted enormous research interest in the past decade and is a well-established area today. (For standard sources, we refer to the survey article by Lee and Preparata [19841 and to the textbooks by Preparata and Shames [1985] and Edelsbrunner [1987bl.) Readers familiar with the literature of computational geometry will have noticed, especially in the last few years, an increasing interest in a geometrical construct called the Voronoi diagram. This trend can also be observed in combinatorial geometry and in a considerable number of articles in natural science journals that address the Voronoi diagram under different names specific to the respective area. Given some number of points in the plane, their Voronoi diagram divides the plane according to the nearest-neighbor

Voronoi diagrams—a survey of a fundamental geometric data structure

The success of the von Neumann model of sequential computation is attributable to the fact that it is an efficient bridge between software and hardware: high-level languages can be efficiently compiled on to this model; yet it can be effeciently implemented in hardware. The author argues that an analogous bridge between software and hardware in required for parallel computation if that is to become as widely used. This article introduces the bulk-synchronous parallel (BSP) model as a candidate for this role, and gives results quantifying its efficiency both in implementing high-level language features and algorithms, as well as in being implemented in hardware.

A bridging model for parallel computation

We consider price-setting algorithms for a simple market in which a seller has an unlimited supply of identical copies of some good, and interacts sequentially with a pool of n buyers, each of whom wants at most one copy of the good. In each transaction, the seller offers a price between 0 and 1, and the buyer decides whether or not to buy, by comparing the offered price to his privately-held valuation for the good. The price offered to a given buyer may be influenced by the outcomes of prior transactions, but each individual buyer participates only once. In this setting, what is the value of knowing the demand curve? In other words, how much revenue can an uninformed seller expect to obtain, relative to a seller with prior information about the buyers' valuations? The answer depends on how the buyers' valuations are modeled. We analyze three cases - identical, random, and worst-case valuations - in each case deriving upper and lower bounds which match within a sublogarithmic factor.

/pdf/the-value-of-knowing-a-demand-curve-bounds-on-regret-for-4pm5ych1m6.pdf

The value of knowing a demand curve: bounds on regret for online posted-price auctions

All previously known algorithms for solving the multicommodity flow problem with capacities are based on linear programming. The best of these algorithms uses a fast matrix multiplication algorithm and takes O(k3.5n3m0.5 log(nDU)) time for the multicommodity flow problem with integer demands and at least O(k2.5n2m0.5 log(n��1DU)) time to find an approximate solution, where k is the number of commodities, n and m denote the number of nodes and edges in the network, D is the largest demand, and U is the largest edge capacity. As a consequence, even multicommodity flow problems with just a few commodities are believed to be much harder than single-commodity maximum-flow or minimum-cost flow problems. In this paper, we describe the first polynomial-time combinatorial algorithms for approximately solving the multicommodity flow problem. The running time of our randomized algorithm is (up to log factors) the same as the time needed to solve k single-commodity flow problems, thus giving the surprising result that approximately computing a k-commodity maximum-flow is not much harder than computing about k single-commodity maximum-flows in isolation. In fact, we prove that a (simple) k-commodity flow problem can be approximately solved by approximately solving O(k log2n) single-commodity minimum-cost flow problems. Our k-commodity algorithm runs in O (knm log4n) time with high probability. We also describe a deterministic algorithm that uses an O(k)-factor more time. Given any multicommodity flow problem as input, both algorithms are guaranteed to provide a feasible solution to a modified flow problem in which all capacities are increased by a (1 + �)-factor, or to provide a proof that there is no feasible solution to the original problem. We also describe faster approximation algorithms for multicommodity flow problems with a special structure, such as those that arise in "sparsest cut" problems and uniform concurrent flow problems.

/pdf/fast-approximation-algorithms-for-multicommodity-flow-4mprs9vwnm.pdf

Fast approximation algorithms for multicommodity flow problems

In this paper, we prove tight upper and lower bounds on the number or processors, information transfer, wire area and time needed to sort N numbers in a bounded-degree fixed-connection network. Our most important new results are: 1) the construction of an O(N))-node bounded-degree network capable of sorting N numbers in O(log N) word steps, 2) a proof that any network capable of sorting N(7 log N)-bit numbers in T bit-steps requires area A where AT2≥ Ω(N2log2N), and 3) the construction of a “small-constant-factor” bounded-degree network that sorts N θ(log N)-bit numbers in T = θ(log N) bit steps with A = θ(N2) area.

Tight bounds on the complexity of parallel sorting

In large distributed networks of computers, it is often the case that a subset of machines wants to cooperate to perform a task. Before they can do so, these machines need to learn of the existence of each other. In this paper we are interested in distributed algorithms whereby machines in a network learn of other machines in the network by making queries to machines they already know. The algorithms should be efficient both in terms of the time required and in terms of the total network communication required until all machines have discovered all other machines. We propose a very simple algorithm called Name-Dropper whereby all machines learn about each other within O(log’ n) rounds with high probability, where n is the number of machines in the network. The total number of connections required is O(n log2 n) and the total number of pointers which must be communicated is O(n2 log2 n), with high probability. Each of the preceding bounds is optimal to within polylogarithmic factors.

/pdf/resource-discovery-in-distributed-networks-35j50sn4ci.pdf

Resource discovery in distributed networks

In this paper, we analyze the behavior of packet-switched communication networks in which packets arrive dynamically at the nodes and are routed in discrete time steps across the edges. We focus on a basic adversarial model of packet arrival and path determination for which the time-averaged arrival rate of packets requiring the use of any edge is limited to be less than 1. This model can reflect the behavior of connection-oriented networks with transient connections (such as ATM networks) as well as connectionless networks (such as the Internet).We concentrate on greedy (also known as work-conserving) contention-resolution protocols. A crucial issue that arises in such a setting is that of stability—will the number of packets in the system remain bounded, as the system runs for an arbitrarily long period of time? We study the universal stability of network (i.e., stability under all greedy protocols) and universal stability of protocols (i.e., stability in all networks). Once the stability of a system is granted, we focus on the two main parameters that characterize its performance: maximum queue size required and maximum end-to-end delay experienced by any packet.Among other things, we show:(i) There exist simple greedy protocols that are stable for all networks.(ii) There exist other commonly used protocols (such as FIFO) and networks (such as arrays and hypercubes) that are not stable.(iii) The n-node ring is stable for all greedy routing protocols (with maximum queue-size and packet delay that is linear in n).(iv) There exists a simple distributed randomized greedy protocol that is stable for all networks and requires only polynomial queue size and polynomial delay.Our results resolve several questions posed by Borodin et al., and provide the first examples of (i) a protocol that is stable for all networks, and (ii) a protocol that is not stable for all networks.

/pdf/universal-stability-results-and-performance-bounds-for-25gcakihau.pdf

Tom Leighton

Papers

The value of knowing a demand curve: bounds on regret for online posted-price auctions

Fast approximation algorithms for multicommodity flow problems

Tight bounds on the complexity of parallel sorting

Resource discovery in distributed networks

Universal-stability results and performance bounds for greedy contention-resolution protocols