Parallel Algorithms for Geometric Graph Problems Alex Andoni (Microsoft Research) Joint with: Aleksandar Nikolov (Rutgers), Krzysztof Onak (IBM), Grigory.

Slides:

Advertisements

Similar presentations

Improved Approximation for the Directed Spanner Problem Grigory Yaroslavtsev Penn State + AT&T Labs - Research (intern) Joint work with Berman (PSU), Bhattacharyya.

Advertisements

Network Design with Degree Constraints Guy Kortsarz Joint work with Rohit Khandekar and Zeev Nutov.

Big Data Reading Group Grigory Yaroslavtsev 361 Levine

1 CSE 980: Data Mining Lecture 16: Hierarchical Clustering.

SkewReduce YongChul Kwon Magdalena Balazinska, Bill Howe, Jerome Rolia* University of Washington, *HP Labs Skew-Resistant Parallel Processing of Feature-Extracting.

Overcoming the L 1 Non- Embeddability Barrier Robert Krauthgamer (Weizmann Institute) Joint work with Alexandr Andoni and Piotr Indyk (MIT)

O(N 1.5 ) divide-and-conquer technique for Minimum Spanning Tree problem Step 1: Divide the graph into  N sub-graph by clustering. Step 2: Solve each.

Backtrack Algorithm for Listing Spanning Trees R. C. Read and R. E. Tarjan (1975) Presented by Levit Vadim.

Data Mining Cluster Analysis: Basic Concepts and Algorithms

Motion Planning CS 6160, Spring 2010 By Gene Peterson 5/4/2010.

Metric Embeddings As Computational Primitives Robert Krauthgamer Weizmann Institute of Science [Based on joint work with Alex Andoni]

Parallel Algorithms for Geometric Graph Problems Grigory Yaroslavtsev 361 Levine STOC 2014, joint work with Alexandr Andoni, Krzysztof.

On Quadtrees for Point Sets Martin Fürer Penn State Joint work with Shiva Kasiviswanathan Martin Fürer Penn State Joint work with Shiva Kasiviswanathan.

Corp. Research Princeton, NJ Computing geodesics and minimal surfaces via graph cuts Yuri Boykov, Siemens Research, Princeton, NJ joint work with Vladimir.

Approximate Counting via Correlation Decay Pinyan Lu Microsoft Research.

Corp. Research Princeton, NJ Cut Metrics and Geometry of Grid Graphs Yuri Boykov, Siemens Research, Princeton, NJ joint work with Vladimir Kolmogorov,

On Sketching Quadratic Forms Robert Krauthgamer, Weizmann Institute of Science Joint with: Alex Andoni, Jiecao Chen, Bo Qin, David Woodruff and Qin Zhang.

DISC-Finder: A distributed algorithm for identifying galaxy clusters.

1 A theory-based decision heuristic for DPLL(T) Dan Goldwasser Ofer Strichman Shai Fine Haifa university TechnionIBM-HRL.

UNC Chapel Hill M. C. Lin Overview of Last Lecture About Final Course Project –presentation, demo, write-up More geometric data structures –Binary Space.

CS 326A: Motion Planning Basic Motion Planning for a Point Robot.

Chapter 5: Path Planning Hadi Moradi. Motivation Need to choose a path for the end effector that avoids collisions and singularities Collisions are easy.

Backtracking Reading Material: Chapter 13, Sections 1, 2, 4, and 5.

Summer School on Hashing’14 Locality Sensitive Hashing Alex Andoni (Microsoft Research)

Basic PRAM algorithms Problem 1. Min of n numbers Problem 2. Computing a position of the first one in the sequence of 0’s and 1’s.

VLSI Physical Design: From Graph Partitioning to Timing Closure Chapter 5: Global Routing © KLMH Lienig 1 FLUTE: Fast Lookup Table Based RSMT Algorithm.

Advanced Topics NP-complete reports. Continue on NP, parallelism.

Distance Approximating Trees in Graphs

Sketching, Sampling and other Sublinear Algorithms: Algorithms for parallel models Alex Andoni (MSR SVC)

© David Kirk/NVIDIA and Wen-mei W. Hwu ECE408/CS483/ECE498al, University of Illinois, ECE408 Applied Parallel Programming Lecture 11 Parallel.

1 Game AI Path Finding. A Common Situation of Game AI A Common Situation of Game AI Path Planning Path Planning –From a start position to a destination.

online convex optimization (with partial information)

Beyond Locality Sensitive Hashing Alex Andoni (Microsoft Research) Joint with: Piotr Indyk (MIT), Huy L. Nguyen (Princeton), Ilya Razenshteyn (MIT)

1 Streaming Algorithms for Geometric Problems Piotr Indyk MIT.

RESOURCES, TRADE-OFFS, AND LIMITATIONS Group 5 8/27/2014.

Optimal Rectangular Partition of a Rectilinear Polygonal Region

Sublinear Algorithms via Precision Sampling Alexandr Andoni (Microsoft Research) joint work with: Robert Krauthgamer (Weizmann Inst.) Krzysztof Onak (CMU)

Fast Fourier Sparsity Testing over the Boolean Hypercube Grigory Yaroslavtsev Joint with Andrew Arnold (Waterloo), Arturs Backurs (MIT),

Sketching, Sampling and other Sublinear Algorithms: Euclidean space: dimension reduction and NNS Alex Andoni (MSR SVC)

11 Algorithmic Techniques for Massive Data (COMS ) Alex Andoni.

Spatial Indexing Techniques Introduction to Spatial Computing CSE 5ISC Some slides adapted from Spatial Databases: A Tour by Shashi Shekhar Prentice Hall.

Graphs and MSTs Sections 1.4 and 9.1. Partial-Order Relations Everybody is not related to everybody. Examples? Direct road connections between locations.

Analysis of the Traveling Salesman Problem and current approaches for solving it. Rishi B. Jethwa and Mayank Agarwal. CSE Department. University of Texas.

High-Performance Computing 12.2: Parallel Algorithms.

What is a metric embedding?Embedding ultrametrics into R d An embedding of an input metric space into a host metric space is a mapping that sends each.

11 Lecture 24: MapReduce Algorithms Wrap-up. Admin PS2-4 solutions Project presentations next week – 20min presentation/team – 10 teams => 3 days – 3.

1 Approximations and Streaming Algorithms for Geometric Problems Piotr Indyk MIT.

ICS 353: Design and Analysis of Algorithms Backtracking King Fahd University of Petroleum & Minerals Information & Computer Science Department.

Distributed Process Discovery From Large Event Logs Sergio Hernández de Mesa {

Sparse RecoveryAlgorithmResults  Original signal x = x k + u, where x k has k large coefficients and u is noise.  Acquire measurements Ax = y. If |x|=n,

Stream-based Geometric Algorithms

Grigory Yaroslavtsev Clustering on Clusters: Massively Parallel Algorithms for Clustering Graphs and Vectors vs Grigory Yaroslavtsev.

Grigory Yaroslavtsev Clustering on Clusters 2049: Massively Parallel Algorithms for Clustering Graphs and Vectors vs Grigory Yaroslavtsev.

Sublinear Algorithmic Tools 3

Distributed Submodular Maximization in Massive Datasets

Here is the graph of a function

Sublinear Algorithmic Tools 2

Lecture 16: Earth-Mover Distance

Parallel Algorithms for Geometric Graph Problems

CIS 700: “algorithms for Big Data”

Sublinear Algorihms for Big Data

Richard Anderson Lecture 28 Coping with NP-Completeness

CSCI B609: “Foundations of Data Science”

Sampling in Graphs: node sparsifiers

Lecture 19 Linear Program

ICS 353: Design and Analysis of Algorithms

Sublinear Algorihms for Big Data

Motivation Contemporary big data tools such as MapReduce and graph processing tools have fixed data abstraction and support a limited set of communication.

ADDITIONAL ANALYSIS TECHNIQUES

Complexity Theory: Foundations

Presentation transcript:

Parallel Algorithms for Geometric Graph Problems Alex Andoni (Microsoft Research) Joint with: Aleksandar Nikolov (Rutgers), Krzysztof Onak (IBM), Grigory Yaroslavtsev (ICERM/Brown)

DATA

Parallel Computing  Systems:  MapReduce [Dean-Ghewamat 2004]  Hadoop [White 2012]  Dryad [Isard etal 2007]  A theory of (modern) parallel computing ?  Model  Algorithmic techniques

Computational Model [Goodrich-Sitchinava-Zhang’11, Beame-Koutris-Suciu’13]

Model Constraints

What about PRAMs ?

Between Log and const… VS

Our problems: Geometric Graphs

Results: MST & EMD algorithms

Framework: Solve-And-Sketch  Partition the space hierarchically in a “nice way”  In each part  Compute a pseudo-solution for the local view  Sketch the pseudo-solution using small space  Send the sketch to be used in the next level/round

MST algorithm: attempt 1  Partition the space hierarchically in a “nice way”  In each part  Compute a pseudo-solution for the local view  Sketch the pseudo-solution using small space  Send the sketch to be used in the next level/round quad trees! local MST send any point as a representative

Difficulties  Quad tree can cut MST edges  forcing irrevocable decisions  Choose a wrong representative

New Partition: Grid Distance

MST Algorithm

VS streaming  Fact: linear streaming => parallel  But: computes cost  e.g., for MST [Indyk’04, Frahling-Indyk-Sohler’05]  Here: actual tree

Earth-Mover Distance

 Partition the space hierarchically in a “nice way”  In each part  Compute a pseudo-solution for the local view  Sketch the pseudo-solution using small space  Send the sketch to be used in the next level/round Solve-And-Sketch Framework for EMD fat quad-tree (as before) & use grid distance after committing to a wrong alternation, cannot get <2 approximation! cannot precompute any “partial solution”

Solve-And-Sketch Framework* for EMD  Partition the space hierarchically in a “nice way”  In each part  Compute a pseudo-solution for the local view  Sketch the pseudo-solution using small space  Send the sketch to be used in the next level/round all solutions

Sketching ALL local solutions

A perspective on EMD

Finale