Many practical computing problems concern large graphs. Standard examples include the Web graph and various social networks. The scale of these graphs - in some cases billions of vertices, trillions of edges - poses challenges to their efficient processing. In this paper we present a computational model suitable for this task. Programs are expressed as a sequence of iterations, in each of which a vertex can receive messages sent in the previous iteration, send messages to other vertices, and modify its own state and that of its outgoing edges or mutate graph topology. This vertex-centric approach is flexible enough to express a broad set of algorithms. The model has been designed for efficient, scalable and fault-tolerant implementation on clusters of thousands of commodity computers, and its implied synchronicity makes reasoning about programs easier. Distribution-related details are hidden behind an abstract API. The result is a framework for processing large graphs that is expressive and easy to program.

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Abstract A balanced binary search tree can be characterized by two orthogonal issues: its search strategy and its balancing strategy. In this paper, we show how to decouple search and balancing strategies so that they can be expressed independently of each other, communicating only by basic operations such as rotations. Different balancing strategies, such as red–black trees and splay trees, and different search applications, such as key search and rank search, can be combined arbitrarily. As a new result, we show how optimal string search can be expressed as a search application on any balanced binary tree. We implement our framework in C++, with the heavy use of templates and inlining. It keeps balancing and searching separate, while still delivering a performance that compares favorably to widely used binary tree implementations. Common services, such as correctness checks and timing measurements, do not have to be rewritten for each tree implementation. The common framework simplifies experimentation with trees and search algorithms; as a demonstration, we present some simple comparisons of red–black trees, splay trees and treaps. Copyright © 2003 John Wiley & Sons, Ltd.