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.

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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

One of the simplest and most popular biophysical models of protein folding is the hydrophobic-hydrophilic (HP) model. The HP model abstracts the hydrophobic interaction in protein folding by labeling the amino acids as hydrophobic (H for nonpolar) or hydrophilic (P for polar). Chains of amino acids are configured as self-avoiding walks on the 3D cubic lattice, where an optimal conformation maximizes the number of adjacencies between H's. In this paper, the protein folding problem under the HP model on the cubic lattice is shown to be NP-complete. This means that the protein folding problem belongs to a large set of problems that are believed to be computationally intractable.

/pdf/protein-folding-in-the-hydrophobic-hydrophilic-hp-is-np-4zr8bjs2d0.pdf

Protein folding in the hydrophobic-hydrophilic (HP) is NP-complete

Making commitments in the face of uncertainty: how to pick a winner almost every time (extended abstract)

This paper presents algorithms for routing channels with L≥2 layers. For the unit vertical overlap model, we describe a two-layer channel routing algorithm that uses at most d + O(√d) tracks to route two-terminal net problems and 2d + O(√d) tracks to route multiterminal nets. We also show that d + Ω(log d) tracks are required to route two-terminal net problems in the worst case even if arbitrary vertical overlap is allowed. We generalize the algorithm to unrestricted multilayer routing and use only d/(L -1) + O(√d/L + 1)> tracks for two-terminal net problems (within O(√d/L + 1) tracks of optimal) and d/(L-2) +O(√d/L + 1) tracks for multiterminal net problems (within a factor of(L-1)/(L-2) times optimal). We demonstrate the generality of our routing strategy by showing that it can be used to duplicate some of the best previous upper bounds for other models (two-layer Manhattan routing and two and three-layer knock-knee routing of two-terminal, two-sided nets), and gives a new upper bound for rotuing with 45-degree diagonal wires.

Nearly optimal algorithms and bounds for multilayer channel routing

The problem of getting the right data to the right place within a reasonable amount of time is one of the most challenging and important tasks facing the designer (and, in some cases, the user) of a large-scale general-purpose parallel machine. This is because the processors comprising a parallel machine need to communicate with each other (or with a common shared memory) in a tightly constrained fashion in order to solve most problems of interest in a timely fashion. Supporting this communication is often an expensive task, in terms of both hardware and time. In fact, most parallel machines devote a significant portion of their resources to handling communication between the processors and the memory.

Methods for message routing in parallel machines

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Tom Leighton

Papers

Protein folding in the hydrophobic-hydrophilic (HP) is NP-complete

Making commitments in the face of uncertainty: how to pick a winner almost every time (extended abstract)

Nearly optimal algorithms and bounds for multilayer channel routing

Methods for message routing in parallel machines

On-line algorithms for path selection in a nonblocking network