PDF-Densest Subgraph in Streaming and MapReduce Bahman Bah

edu Ravi Kumar Yahoo Research Sunnyvale CA ravikumaryahooinccom Sergei Vassilvitskii Yahoo Research New York NY sergeiyahooinccom ABSTRACT The problem of nding locally dense components of a graph is an important primitive in data analysis with widera. There is a signi64257cant gap between the best known upper and lower bounds for this problem It is NPhard and does not have a PTAS unless NP has subexponential time algorithms On the other hand the current best known algorithm of Feige Kortsarz and Both results are of similar avor ruling out constant factor approximations in polynomial time for the D S problem under an average case hardness assumption The rst result asserts that if Random AND formulas are hard to distinguish from ones that are ESSAY REVISION. ESSAY PLANNING Q AND A. TIMED ESSAY ON THEORIES OF EDUCATION. COFFEE BREAK. INTRODUCTION TO LABELLING AND STREAMING –ACTIVITY. PP SLIDES: STREAMING /LABELLING HARGREAVES AND BALL. ESSAY AND EXAM PLANNING. Extracting Optimal Quasi-Cliques with Quality . Guarantees. . Charalampos (Babis) E. Tsourakakis. charalampos.tsourakakis@aalto.fi. KDD 2013. and . Hadoop. Debapriyo Majumdar. Data Mining – Fall 2014. Indian Statistical Institute Kolkata. November 10, 2014. Let’s keep the intro short. Modern data mining: process immense amount of data quickly. Degree 10 0 10 1 10 2 10 3 10 4 10 5 10 0 10 2 10 4 10 6 Total Subgraph 1 Subgraph 2 Subgraph 3 Degree 10 0 10 1 10 2 10 3 10 4 10 5 Count of Degree 10 0 10 2 10 4 10 6 Total Subgraph 1 Subgraph 2 Sub 10 ].However,frequentlythedensestsubgraphprob-lemfailsindetectinglargenear-cliquesinnetworks.Inthiswork,weintroducethe-cliquedensestsubgraphproblem,2.Thisgeneralizesthewellstudieddens-estsubgraphprobl Simplified Data Processing on Large . Clusters. by Jeffrey Dean and Sanjay . Ghemawa. Presented by Jon Logan. Outline. Problem Statement / Motivation. An Example Program. MapReduce. . vs. Hadoop. GFS / HDFS. Parallel Computing. MapReduce. Examples. Parallel Efficiency. Assignment. Parallel Computing. Parallel efficiency with . p. processors. Traditional parallel computing:. focus on compute intensive tasks. (and related problems). on Minor-Free Graphs. Hans . Bodlaender. (U Utrecht, TU Eindhoven). Jesper. . Nederlof. (TU Eindhoven). Tom van der . Zanden. (U Utrecht). 1. Subgraph Isomorphism. Given: a . Extracting Optimal Quasi-Cliques with Quality . Guarantees. . Charalampos (Babis) E. Tsourakakis. charalampos.tsourakakis@aalto.fi. KDD 2013. Longin Jan Latecki. Based on :. P. . Dupont. , J. . Callut. , G. Dooms, J.-N. . Monette. and Y. Deville.. Relevant subgraph extraction from random walks in a graph. . RR 2006-07, Catholic University of Louvain , November 2006.. Jimmy Lin. The iSchool. University of Maryland. Monday, March 30, 2009. This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States. See http://creativecommons.org/licenses/by-nc-sa/3.0/us/ for details. Source. MapReduce. : Simplified Data Processing in Large Clusters. . Jefferey. Dean and Sanjay . Ghemawat. . OSDI 2004. Example Scenario. 3. Genome data from roughly . one million users. 125 MB of data per user.