We give algorithms for geometric graph problems in the modern parallel models such as MapReduce [DG04, KSV10, GSZ11, BKS13]. For example, for the Minimum Spanning Tree (MST) problem over a set of points in the two-dimensional space, our algorithm computes a (1 + )-approximate MST. Our algorithms

computational rule, the sum-product algorithm operates in factor graphs to compute---either exactly or approximately---various marginal functions by distributed message-passing in the graph. A wide variety of algorithms developed in artificial intelligence, signal processing, and digital communications can

as follows: ffl We devise a model for dynamic graph algorithms, based on performing queries and updates on an implicit representation of the drawing, and we show its applications. ffl We present several efficient dynamic drawing algorithms for trees, series-parallel digraphs, planar st-digraphs, and planar

In this paper we explore some implications of view-ing graphs as geometric objects. This approach of-fers a new perspective on a number of graph-theoretic and algorithmic problems. There are several ways to model graphs geometrically and our main concern here is with geometric representations

. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers -- the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows

The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices

Randomized algorithms, once viewed as a tool in computational number theory, have by now found widespread application. Growth has been fueled by the two major benefits of randomization: simplicity and speed. For many applications a randomized algorithm is the fastest algorithm available

This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning

We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2-satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds

The value of depth-first search or "backtracking" as a technique for solving problems is illustrated by two examples. An improved version of an algorithm for finding the strongly connected components of a directed graph and ar algorithm for finding the biconnected components