Algorithmic Aspects of Big Data. Nikhil Bansal (TU Eindhoven)


 Horatio Morrison
 3 years ago
 Views:
Transcription
1 Algorithmic Aspects of Big Data Nikhil Bansal (TU Eindhoven)
2 Algorithm design Algorithm: Set of steps to solve a problem (by a computer) Studied since 1950 s. Given a problem: Find (i) best solution (ii) quickly Traveling salesman problem (TSP) n! possibilities ( for n=60) Ideally: Polynomial running time (n 2, n 3 ) 33 cities, 1962 competition
3 70 s: Problems Polynomial time (n log n, n 2,n 3 ) E.g. Shortest path, matching, maxflow,... NPHard: TSP + most other problems (brute force 2 n = only option) Late 80 snow: Coping with NPhardness Approximation algorithms: Even if NPHard, may be a 95% optimal solution can be found in polynomial time? (very rich theory/connections) Heuristic Approaches: (often successful in practice)
4 Heuristic methods (TSP) 120 Germany, USA, ,509 USA, ,978 Sweden, ,900 VLSI ,000 USA, still unsolved
5 Tools seemed quite powerful Tools Problems
6 Last few years
7 Google: Billions of webpages Example Figure out which documents are similar (various reasons: show diverse pages for a query) Polynomial/nonpolynomial view is too limited (Even n 2 time is prohibitive for huge n) Don t care about perfect answer. Pages change/disappear, No perfect notion of similarity anyway Want a quick solution. Some error is alright.
8 Example 2 Facebook: Which 10,000 users (among many millions) should be shown this ad? Want a quick solution. Some error is alright.
9 Very different questions Needed: Totally new ways of thinking Discard old beliefs Beautiful new ideas emerging
10 Rest of the talk A glimpse of some ideas 1) Counting distinct elements 2) Correlation Clustering 3) Local Partitioning Concluding Remarks
11 Counting distinct elements Input: Stream of numbers (say in range [1,n] ) Example: Goal: Compute number of distinct elements. Here 5 because we saw {3,4,2,17,11} Simple Solution: Just maintain a list of items seen thus far Stream: List: { }
12 Counting distinct elements Input: Stream of numbers (say in range [1,n] ) Example: Goal: Compute number of distinct elements. Here 5 because we saw {3,4,2,17,11} Simple Solution: Just maintain a list of items seen thus far Stream: List: { 3 }
13 Counting distinct elements Input: Stream of numbers (say in range [1,n] ) Example: Goal: Compute number of distinct elements. Here 5 because we saw {3,4,2,17,11} Simple Solution: Just maintain a list of items seen thus far Stream: List: { 3, 4}
14 Counting distinct elements Input: Stream of numbers (say in range [1,n] ) Example: Goal: Compute number of distinct elements. Here 5 because we saw {3,4,2,17,11} Simple Solution: Just maintain a list of items seen thus far Stream: List: { 3, 4}
15 Counting distinct elements Input: Stream of numbers (say in range [1,n] ) Example: Goal: Compute number of distinct elements. Here 5 because we saw {3,4,2,17,11} Simple Solution: Just maintain a list of items seen thus far Stream: List: { 3, 4, 2}
16 Counting Distinct elements Note: The algorithm tracks the numbers seen thus far. Question: What if it can remember only 1 number? (very limited memory) Trouble: Can barely remember anything about past. Stream: When you scan next element, no clue if already seen?
17 Seems completely hopeless? Intuition only partly right Cannot hope to count exactly. But who cares if answer is 3,425,269 or 3,425,587? Approximate counting possible!! Technique: Minhashing (beautiful use of approximation and randomization)
18 Number of distinct elements Basic Idea [FlajoletMartin 82]: Use a random hash function (map). (e.g. encryption function) h:[1,n] > [1,n ] say n >> n Algorithm: Keep track of min h(i) Stream = h(2) n n
19 Number of distinct elements Basic Idea [FlajoletMartin 82]: Use a random hash function (map). (e.g. encryption function) h:[1,n] > [1,n ] say n >> n Algorithm: Keep track of min h(i) Stream = h(8) n n
20 Number of distinct elements Basic Idea [FlajoletMartin 82]: Use a random hash function (map). (e.g. encryption function) h:[1,n] > [1,n ] say n >> n Algorithm: Keep track of min h(i) Stream = h(8) n n Note: h(i) is same every time i is encountered.
21 Number of distinct elements Basic Idea [FlajoletMartin 82]: Use a random hash function (map). (e.g. encryption function) h:[1,n] > [1,n ] say n >> n Algorithm: Keep track of min h(i) Stream = h(8) n n Note: h(i) is same every time i is encountered.
22 Number of distinct elements Keep track of min h(i) Suppose 1 distinct element (stream = ) Min h(i) n / n n 1 n
23 Number of distinct elements Keep track of min h(i) Suppose 2 distinct elements Min h(i) n / n n 1 n If k items seen, expect minvalue to be around n /(k+1) Solution: Estimate of # elements = n / min h(i) 1
24 Number of distinct elements Randomness could mess things up. E.g. May just 1 element, But min(h(i)) could be far. expect min(h(i)) = n /2 Standard trick: O(1) such hash functions, take median entry. Theorem: For any ε > 0, can estimate distinct elements to within 1 ± ε factor accuracy with high probability. Space = O 1 ε 2
25 A closer look Random hash function h. We need that h(i) value be same every time we see i. One has to store each h(i) some where. h(1), h(2), h(3),, h(n) need n log n space?? Did we just disguise our inherent problem? There is a fix! Key idea: Do not need full power of randomness
26 What is randomness? Do not need full randomness Pairwise independence: For any a 1, a 2, x 1, x 2 Pr [ h(x 1 ) = a 1 and h(x 2 ) = a 2 ] = 1/n n n Such an h is very simple to store h(x) = ax + b mod (p) [just need to store a and b]
27 MinHashing: Applications Similarity of Web pages (if mostly similar words) Google: Page > Few minhash values (few bits) Similar page detection: quadratic > Linear time Sketching Complex Simple Tons of amazing applications ( several researchers )
28 Correlation Clustering (new model motivated by big data)
29 Clustering Cluster documents by topic Cluster users by items bought One of the most fundamental operations in data mining Traditional Approach: Objects > points in some high dim. space Some distance function Some objective (kmedian, kmeans, ) Hope something useful comes out
30 Clustering Document clustering: Bag of words (traditional approach) Another approach (Bansal, Blum, Chawla) Correlation Clustering: Clustering via pairwise similarity. Classifier: Takes two documents and tells how similar they are dissimilar Doc 1 Doc 2 similar Idea: Use this classifier for clustering.
31 Correlation Clustering E.g. Run classifier on every pair of items dissimilar similar
32 In general, there could be inconsistencies dissimilar similar Any clustering, disagrees on at least one edge
33 In general, there could be inconsistencies dissimilar similar Any clustering, disagrees on at least one edge
34 In general, there could be inconsistencies dissimilar similar Any clustering, disagrees on at least one edge Goal: Find clustering agreeing on most edges Interesting approximation algorithms Quite successful Several extensions (not all pairs, which pair to probe, )
35 Local Partitioning (Light Networks, Philips)
36 Light Networks Wireless capability: Control, monitor, exchange performance data Segment controller for a region
37 Light Networks Goal: Partition network in pieces, s.t. each piece (i) Good intraconnectvity (ii) Roughly equal size (iii) Small diameter (few hops) (iv) Low failure probability Impossible to approach via traditional algorithms Idea (Bansal, Leeuwaarden, Mathijsen) Local partitioning algorithms are easy to tailor.
38 Local Partitioning Algorithms Studied by SpielmanTeng and AndersenPeres (inspired by big data) Find a wellconnected piece containing node v. v Time proportional to size of output piece
39 Local Algorithms
40 Local Algorithms
41 Local Algorithms
42 Local Algorithms Details: Poster of Britt Mathijsen
43 Concluding Remarks Very small glimpse (streaming and sketching, statistical learning, machine learning, dealing with noisy data, sublinear algorithms, ) Exciting new algorithmic problems 1) Huge impact 2) Beautiful ideas 3) Interdisciplinary DSCE a platform to bring diverse groups and skills together
44 Thanks for your attention!
B490 Mining the Big Data. 0 Introduction
B490 Mining the Big Data 0 Introduction Qin Zhang 11 Data Mining What is Data Mining? A definition : Discovery of useful, possibly unexpected, patterns in data. 21 Data Mining What is Data Mining? A
More informationDistance Degree Sequences for Network Analysis
Universität Konstanz Computer & Information Science Algorithmics Group 15 Mar 2005 based on Palmer, Gibbons, and Faloutsos: ANF A Fast and Scalable Tool for Data Mining in Massive Graphs, SIGKDD 02. Motivation
More informationBig Data & Scripting Part II Streaming Algorithms
Big Data & Scripting Part II Streaming Algorithms 1, 2, a note on sampling and filtering sampling: (randomly) choose a representative subset filtering: given some criterion (e.g. membership in a set),
More informationNimble Algorithms for Cloud Computing. Ravi Kannan, Santosh Vempala and David Woodruff
Nimble Algorithms for Cloud Computing Ravi Kannan, Santosh Vempala and David Woodruff Cloud computing Data is distributed arbitrarily on many servers Parallel algorithms: time Streaming algorithms: sublinear
More informationComputer Algorithms. NPComplete Problems. CISC 4080 Yanjun Li
Computer Algorithms NPComplete Problems NPcompleteness The quest for efficient algorithms is about finding clever ways to bypass the process of exhaustive search, using clues from the input in order
More informationMapReduce and Distributed Data Analysis. Sergei Vassilvitskii Google Research
MapReduce and Distributed Data Analysis Google Research 1 Dealing With Massive Data 2 2 Dealing With Massive Data Polynomial Memory Sublinear RAM Sketches External Memory Property Testing 3 3 Dealing With
More information1 Message Authentication
Theoretical Foundations of Cryptography Lecture Georgia Tech, Spring 200 Message Authentication Message Authentication Instructor: Chris Peikert Scribe: Daniel Dadush We start with some simple questions
More informationA Working Knowledge of Computational Complexity for an Optimizer
A Working Knowledge of Computational Complexity for an Optimizer ORF 363/COS 323 Instructor: Amir Ali Ahmadi TAs: Y. Chen, G. Hall, J. Ye Fall 2014 1 Why computational complexity? What is computational
More informationIntroduction to computer science
Introduction to computer science Michael A. Nielsen University of Queensland Goals: 1. Introduce the notion of the computational complexity of a problem, and define the major computational complexity classes.
More informationChapter 11. 11.1 Load Balancing. Approximation Algorithms. Load Balancing. Load Balancing on 2 Machines. Load Balancing: Greedy Scheduling
Approximation Algorithms Chapter Approximation Algorithms Q. Suppose I need to solve an NPhard problem. What should I do? A. Theory says you're unlikely to find a polytime algorithm. Must sacrifice one
More informationData Science Center Eindhoven. Big Data: Challenges and Opportunities for Mathematicians. Alessandro Di Bucchianico
Data Science Center Eindhoven Big Data: Challenges and Opportunities for Mathematicians Alessandro Di Bucchianico Dutch Mathematical Congress April 15, 2015 Contents 1. Big Data terminology 2. Various
More informationCloud and Big Data Summer School, Stockholm, Aug., 2015 Jeffrey D. Ullman
Cloud and Big Data Summer School, Stockholm, Aug., 2015 Jeffrey D. Ullman To motivate the Bloomfilter idea, consider a web crawler. It keeps, centrally, a list of all the URL s it has found so far. It
More informationBig Data & Scripting Part II Streaming Algorithms
Big Data & Scripting Part II Streaming Algorithms 1, Counting Distinct Elements 2, 3, counting distinct elements problem formalization input: stream of elements o from some universe U e.g. ids from a set
More informationSIMS 255 Foundations of Software Design. Complexity and NPcompleteness
SIMS 255 Foundations of Software Design Complexity and NPcompleteness Matt Welsh November 29, 2001 mdw@cs.berkeley.edu 1 Outline Complexity of algorithms Space and time complexity ``Big O'' notation Complexity
More informationUniversal hashing. In other words, the probability of a collision for two different keys x and y given a hash function randomly chosen from H is 1/m.
Universal hashing No matter how we choose our hash function, it is always possible to devise a set of keys that will hash to the same slot, making the hash scheme perform poorly. To circumvent this, we
More informationLecture 10: Regression Trees
Lecture 10: Regression Trees 36350: Data Mining October 11, 2006 Reading: Textbook, sections 5.2 and 10.5. The next three lectures are going to be about a particular kind of nonlinear predictive model,
More informationScalable Machine Learning  or what to do with all that Big Data infrastructure
 or what to do with all that Big Data infrastructure TU Berlin blog.mikiobraun.de Strata+Hadoop World London, 2015 1 Complex Data Analysis at Scale Clickthrough prediction Personalized Spam Detection
More information16.1 MAPREDUCE. For personal use only, not for distribution. 333
For personal use only, not for distribution. 333 16.1 MAPREDUCE Initially designed by the Google labs and used internally by Google, the MAPREDUCE distributed programming model is now promoted by several
More informationMapReduce Algorithms. Sergei Vassilvitskii. Saturday, August 25, 12
MapReduce Algorithms A Sense of Scale At web scales... Mail: Billions of messages per day Search: Billions of searches per day Social: Billions of relationships 2 A Sense of Scale At web scales... Mail:
More informationB669 Sublinear Algorithms for Big Data
B669 Sublinear Algorithms for Big Data Qin Zhang 11 Now about the Big Data Big data is everywhere : over 2.5 petabytes of sales transactions : an index of over 19 billion web pages : over 40 billion of
More informationAnalysis of MapReduce Algorithms
Analysis of MapReduce Algorithms Harini Padmanaban Computer Science Department San Jose State University San Jose, CA 95192 4089241000 harini.gomadam@gmail.com ABSTRACT MapReduce is a programming model
More informationLecture 4 Online and streaming algorithms for clustering
CSE 291: Geometric algorithms Spring 2013 Lecture 4 Online and streaming algorithms for clustering 4.1 Online kclustering To the extent that clustering takes place in the brain, it happens in an online
More informationBig Data Technology MapReduce Motivation: Indexing in Search Engines
Big Data Technology MapReduce Motivation: Indexing in Search Engines Edward Bortnikov & Ronny Lempel Yahoo Labs, Haifa Indexing in Search Engines Information Retrieval s two main stages: Indexing process
More informationComplexity Theory. IE 661: Scheduling Theory Fall 2003 Satyaki Ghosh Dastidar
Complexity Theory IE 661: Scheduling Theory Fall 2003 Satyaki Ghosh Dastidar Outline Goals Computation of Problems Concepts and Definitions Complexity Classes and Problems Polynomial Time Reductions Examples
More informationSocial Media Mining. Data Mining Essentials
Introduction Data production rate has been increased dramatically (Big Data) and we are able store much more data than before E.g., purchase data, social media data, mobile phone data Businesses and customers
More information! Solve problem to optimality. ! Solve problem in polytime. ! Solve arbitrary instances of the problem. #approximation algorithm.
Approximation Algorithms 11 Approximation Algorithms Q Suppose I need to solve an NPhard problem What should I do? A Theory says you're unlikely to find a polytime algorithm Must sacrifice one of three
More informationCloud and Big Data Summer School, Stockholm, Aug. 2015 Jeffrey D. Ullman
Cloud and Big Data Summer School, Stockholm, Aug. 2015 Jeffrey D. Ullman 2 In a DBMS, input is under the control of the programming staff. SQL INSERT commands or bulk loaders. Stream management is important
More informationApplied Algorithm Design Lecture 5
Applied Algorithm Design Lecture 5 Pietro Michiardi Eurecom Pietro Michiardi (Eurecom) Applied Algorithm Design Lecture 5 1 / 86 Approximation Algorithms Pietro Michiardi (Eurecom) Applied Algorithm Design
More informationB490 Mining the Big Data. 2 Clustering
B490 Mining the Big Data 2 Clustering Qin Zhang 11 Motivations Group together similar documents/webpages/images/people/proteins/products One of the most important problems in machine learning, pattern
More informationAnalyzing the Facebook graph?
Logistics Big Data Algorithmic Introduction Prof. Yuval Shavitt Contact: shavitt@eng.tau.ac.il Final grade: 4 6 home assignments (will try to include programing assignments as well): 2% Exam 8% Big Data
More informationNPCompleteness I. Lecture 19. 19.1 Overview. 19.2 Introduction: Reduction and Expressiveness
Lecture 19 NPCompleteness I 19.1 Overview In the past few lectures we have looked at increasingly more expressive problems that we were able to solve using efficient algorithms. In this lecture we introduce
More informationOutline. NPcompleteness. When is a problem easy? When is a problem hard? Today. Euler Circuits
Outline NPcompleteness Examples of Easy vs. Hard problems Euler circuit vs. Hamiltonian circuit Shortest Path vs. Longest Path 2pairs sum vs. general Subset Sum Reducing one problem to another Clique
More informationGraph Theory and Complex Networks: An Introduction. Chapter 08: Computer networks
Graph Theory and Complex Networks: An Introduction Maarten van Steen VU Amsterdam, Dept. Computer Science Room R4.20, steen@cs.vu.nl Chapter 08: Computer networks Version: March 3, 2011 2 / 53 Contents
More informationInfrastructures for big data
Infrastructures for big data Rasmus Pagh 1 Today s lecture Three technologies for handling big data: MapReduce (Hadoop) BigTable (and descendants) Data stream algorithms Alternatives to (some uses of)
More information6.080 / 6.089 Great Ideas in Theoretical Computer Science Spring 2008
MIT OpenCourseWare http://ocw.mit.edu 6.080 / 6.089 Great Ideas in Theoretical Computer Science Spring 008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
More informationMining Data Streams. Chapter 4. 4.1 The Stream Data Model
Chapter 4 Mining Data Streams Most of the algorithms described in this book assume that we are mining a database. That is, all our data is available when and if we want it. In this chapter, we shall make
More information! Solve problem to optimality. ! Solve problem in polytime. ! Solve arbitrary instances of the problem. !approximation algorithm.
Approximation Algorithms Chapter Approximation Algorithms Q Suppose I need to solve an NPhard problem What should I do? A Theory says you're unlikely to find a polytime algorithm Must sacrifice one of
More informationUse of Data Mining Techniques to Improve the Effectiveness of Sales and Marketing
Available Online at www.ijcsmc.com International Journal of Computer Science and Mobile Computing A Monthly Journal of Computer Science and Information Technology IJCSMC, Vol. 4, Issue. 4, April 2015,
More informationCAS CS 565, Data Mining
CAS CS 565, Data Mining Course logistics Course webpage: http://www.cs.bu.edu/~evimaria/cs56510.html Schedule: Mon Wed, 45:30 Instructor: Evimaria Terzi, evimaria@cs.bu.edu Office hours: Mon 2:304pm,
More informationTopological Properties
Advanced Computer Architecture Topological Properties Routing Distance: Number of links on route Node degree: Number of channels per node Network diameter: Longest minimum routing distance between any
More informationFUZZY CLUSTERING ANALYSIS OF DATA MINING: APPLICATION TO AN ACCIDENT MINING SYSTEM
International Journal of Innovative Computing, Information and Control ICIC International c 0 ISSN 3448 Volume 8, Number 8, August 0 pp. 4 FUZZY CLUSTERING ANALYSIS OF DATA MINING: APPLICATION TO AN ACCIDENT
More informationLecture 3: Linear methods for classification
Lecture 3: Linear methods for classification Rafael A. Irizarry and Hector Corrada Bravo February, 2010 Today we describe four specific algorithms useful for classification problems: linear regression,
More informationPrivate Approximation of Clustering and Vertex Cover
Private Approximation of Clustering and Vertex Cover Amos Beimel, Renen Hallak, and Kobbi Nissim Department of Computer Science, BenGurion University of the Negev Abstract. Private approximation of search
More informationPSG College of Technology, Coimbatore641 004 Department of Computer & Information Sciences BSc (CT) G1 & G2 Sixth Semester PROJECT DETAILS.
PSG College of Technology, Coimbatore641 004 Department of Computer & Information Sciences BSc (CT) G1 & G2 Sixth Semester PROJECT DETAILS Project Project Title Area of Abstract No Specialization 1. Software
More informationLecture 9  Message Authentication Codes
Lecture 9  Message Authentication Codes Boaz Barak March 1, 2010 Reading: BonehShoup chapter 6, Sections 9.1 9.3. Data integrity Until now we ve only been interested in protecting secrecy of data. However,
More informationFile Management. Chapter 12
Chapter 12 File Management File is the basic element of most of the applications, since the input to an application, as well as its output, is usually a file. They also typically outlive the execution
More informationKNIME TUTORIAL. Anna Monreale KDDLab, University of Pisa Email: annam@di.unipi.it
KNIME TUTORIAL Anna Monreale KDDLab, University of Pisa Email: annam@di.unipi.it Outline Introduction on KNIME KNIME components Exercise: Market Basket Analysis Exercise: Customer Segmentation Exercise:
More informationExtreme Computing. Big Data. Stratis Viglas. School of Informatics University of Edinburgh sviglas@inf.ed.ac.uk. Stratis Viglas Extreme Computing 1
Extreme Computing Big Data Stratis Viglas School of Informatics University of Edinburgh sviglas@inf.ed.ac.uk Stratis Viglas Extreme Computing 1 Petabyte Age Big Data Challenges Stratis Viglas Extreme Computing
More informationStatistical Learning Theory Meets Big Data
Statistical Learning Theory Meets Big Data Randomized algorithms for frequent itemsets Eli Upfal Brown University Data, data, data In God we trust, all others (must) bring data Prof. W.E. Deming, Statistician,
More informationprinceton univ. F 13 cos 521: Advanced Algorithm Design Lecture 6: Provable Approximation via Linear Programming Lecturer: Sanjeev Arora
princeton univ. F 13 cos 521: Advanced Algorithm Design Lecture 6: Provable Approximation via Linear Programming Lecturer: Sanjeev Arora Scribe: One of the running themes in this course is the notion of
More informationDiscuss the size of the instance for the minimum spanning tree problem.
3.1 Algorithm complexity The algorithms A, B are given. The former has complexity O(n 2 ), the latter O(2 n ), where n is the size of the instance. Let n A 0 be the size of the largest instance that can
More informationPart 2: Community Detection
Chapter 8: Graph Data Part 2: Community Detection Based on Leskovec, Rajaraman, Ullman 2014: Mining of Massive Datasets Big Data Management and Analytics Outline Community Detection  Social networks 
More informationDiversity Coloring for Distributed Data Storage in Networks 1
Diversity Coloring for Distributed Data Storage in Networks 1 Anxiao (Andrew) Jiang and Jehoshua Bruck California Institute of Technology Pasadena, CA 9115, U.S.A. {jax, bruck}@paradise.caltech.edu Abstract
More informationU.C. Berkeley CS276: Cryptography Handout 0.1 Luca Trevisan January, 2009. Notes on Algebra
U.C. Berkeley CS276: Cryptography Handout 0.1 Luca Trevisan January, 2009 Notes on Algebra These notes contain as little theory as possible, and most results are stated without proof. Any introductory
More informationVEHICLE ROUTING PROBLEM
VEHICLE ROUTING PROBLEM Readings: E&M 0 Topics: versus TSP Solution methods Decision support systems for Relationship between TSP and Vehicle routing problem () is similar to the Traveling salesman problem
More informationGuessing Game: NPComplete?
Guessing Game: NPComplete? 1. LONGESTPATH: Given a graph G = (V, E), does there exists a simple path of length at least k edges? YES 2. SHORTESTPATH: Given a graph G = (V, E), does there exists a simple
More informationP vs NP problem in the field anthropology
Research Article P vs NP problem in the field anthropology Michael.A. Popov, Oxford, UK Email Michael282.eps@gmail.com Keywords P =?NP  complexity anthropology  M decision  quantum like game  gametheoretical
More informationA Sublinear Bipartiteness Tester for Bounded Degree Graphs
A Sublinear Bipartiteness Tester for Bounded Degree Graphs Oded Goldreich Dana Ron February 5, 1998 Abstract We present a sublineartime algorithm for testing whether a bounded degree graph is bipartite
More informationA Modified KMeans Clustering with a DensitySensitive Distance Metric
A Modified KMeans Clustering with a DensitySensitive Distance Metric Ling Wang, Liefeng Bo, Licheng Jiao Institute of Intelligent Information Processing, Xidian University Xi an 710071, China {wliiip,blf0218}@163.com,
More informationEfficiency of algorithms. Algorithms. Efficiency of algorithms. Binary search and linear search. Best, worst and average case.
Algorithms Efficiency of algorithms Computational resources: time and space Best, worst and average case performance How to compare algorithms: machineindependent measure of efficiency Growth rate Complexity
More informationData Structures in Java. Session 15 Instructor: Bert Huang http://www1.cs.columbia.edu/~bert/courses/3134
Data Structures in Java Session 15 Instructor: Bert Huang http://www1.cs.columbia.edu/~bert/courses/3134 Announcements Homework 4 on website No class on Tuesday Midterm grades almost done Review Indexing
More informationOffline sorting buffers on Line
Offline sorting buffers on Line Rohit Khandekar 1 and Vinayaka Pandit 2 1 University of Waterloo, ON, Canada. email: rkhandekar@gmail.com 2 IBM India Research Lab, New Delhi. email: pvinayak@in.ibm.com
More informationCSEE5430 Scalable Cloud Computing Lecture 2
CSEE5430 Scalable Cloud Computing Lecture 2 Keijo Heljanko Department of Computer Science School of Science Aalto University keijo.heljanko@aalto.fi 14.92015 1/36 Google MapReduce A scalable batch processing
More informationNear Optimal Solutions
Near Optimal Solutions Many important optimization problems are lacking efficient solutions. NPComplete problems unlikely to have polynomial time solutions. Good heuristics important for such problems.
More informationWellSeparated Pair Decomposition for the Unitdisk Graph Metric and its Applications
WellSeparated Pair Decomposition for the Unitdisk Graph Metric and its Applications Jie Gao Department of Computer Science Stanford University Joint work with Li Zhang Systems Research Center HewlettPackard
More information1 Formulating The Low Degree Testing Problem
6.895 PCP and Hardness of Approximation MIT, Fall 2010 Lecture 5: Linearity Testing Lecturer: Dana Moshkovitz Scribe: Gregory Minton and Dana Moshkovitz In the last lecture, we proved a weak PCP Theorem,
More informationAlgorithmic Techniques for Big Data Analysis. Barna Saha AT&T LabResearch
Algorithmic Techniques for Big Data Analysis Barna Saha AT&T LabResearch Challenges of Big Data VOLUME Large amount of data VELOCITY Needs to be analyzed quickly VARIETY Different types of structured
More informationDistributed Computing over Communication Networks: Topology. (with an excursion to P2P)
Distributed Computing over Communication Networks: Topology (with an excursion to P2P) Some administrative comments... There will be a Skript for this part of the lecture. (Same as slides, except for today...
More informationIntroduction to Logic in Computer Science: Autumn 2006
Introduction to Logic in Computer Science: Autumn 2006 Ulle Endriss Institute for Logic, Language and Computation University of Amsterdam Ulle Endriss 1 Plan for Today Now that we have a basic understanding
More informationMachine Learning using MapReduce
Machine Learning using MapReduce What is Machine Learning Machine learning is a subfield of artificial intelligence concerned with techniques that allow computers to improve their outputs based on previous
More informationThe Classes P and NP
The Classes P and NP We now shift gears slightly and restrict our attention to the examination of two families of problems which are very important to computer scientists. These families constitute the
More informationLecture 10: Distinct Degree Factoring
CS681 Computational Number Theory Lecture 10: Distinct Degree Factoring Instructor: Piyush P Kurur Scribe: Ramprasad Saptharishi Overview Last class we left of with a glimpse into distant degree factorization.
More informationNoSQL. Thomas Neumann 1 / 22
NoSQL Thomas Neumann 1 / 22 What are NoSQL databases? hard to say more a theme than a well defined thing Usually some or all of the following: no SQL interface no relational model / no schema no joins,
More informationMining SocialNetwork Graphs
342 Chapter 10 Mining SocialNetwork Graphs There is much information to be gained by analyzing the largescale data that is derived from social networks. The bestknown example of a social network is
More informationWhat mathematical optimization can, and cannot, do for biologists. Steven Kelk Department of Knowledge Engineering (DKE) Maastricht University, NL
What mathematical optimization can, and cannot, do for biologists Steven Kelk Department of Knowledge Engineering (DKE) Maastricht University, NL Introduction There is no shortage of literature about the
More informationSecurityAware Beacon Based Network Monitoring
SecurityAware Beacon Based Network Monitoring Masahiro Sasaki, Liang Zhao, Hiroshi Nagamochi Graduate School of Informatics, Kyoto University, Kyoto, Japan Email: {sasaki, liang, nag}@amp.i.kyotou.ac.jp
More informationIntroduction to Hadoop and MapReduce
Introduction to Hadoop and MapReduce THE CONTRACTOR IS ACTING UNDER A FRAMEWORK CONTRACT CONCLUDED WITH THE COMMISSION Largescale Computation Traditional solutions for computing large quantities of data
More informationCS335 Sample Questions for Exam #2
CS335 Sample Questions for Exam #2.) Compare connectionoriented with connectionless protocols. What type of protocol is IP? How about TCP and UDP? Connectionoriented protocols Require a setup time to
More informationClustering. 15381 Artificial Intelligence Henry Lin. Organizing data into clusters such that there is
Clustering 15381 Artificial Intelligence Henry Lin Modified from excellent slides of Eamonn Keogh, Ziv BarJoseph, and Andrew Moore What is Clustering? Organizing data into clusters such that there is
More informationNotes on Complexity Theory Last updated: August, 2011. Lecture 1
Notes on Complexity Theory Last updated: August, 2011 Jonathan Katz Lecture 1 1 Turing Machines I assume that most students have encountered Turing machines before. (Students who have not may want to look
More informationDATA ANALYSIS IN PUBLIC SOCIAL NETWORKS
International Scientific Conference & International Workshop Present Day Trends of Innovations 2012 28 th 29 th May 2012 Łomża, Poland DATA ANALYSIS IN PUBLIC SOCIAL NETWORKS Lubos Takac 1 Michal Zabovsky
More informationMultimedia Databases. WolfTilo Balke Philipp Wille Institut für Informationssysteme Technische Universität Braunschweig http://www.ifis.cs.tubs.
Multimedia Databases WolfTilo Balke Philipp Wille Institut für Informationssysteme Technische Universität Braunschweig http://www.ifis.cs.tubs.de 14 Previous Lecture 13 Indexes for Multimedia Data 13.1
More informationCategorical Data Visualization and Clustering Using Subjective Factors
Categorical Data Visualization and Clustering Using Subjective Factors ChiaHui Chang and ZhiKai Ding Department of Computer Science and Information Engineering, National Central University, ChungLi,
More informationAdvanced Big Data Analytics with R and Hadoop
REVOLUTION ANALYTICS WHITE PAPER Advanced Big Data Analytics with R and Hadoop 'Big Data' Analytics as a Competitive Advantage Big Analytics delivers competitive advantage in two ways compared to the traditional
More informationThe LCA Problem Revisited
The LA Problem Revisited Michael A. Bender Martín Faracholton SUNY Stony Brook Rutgers University May 16, 2000 Abstract We present a very simple algorithm for the Least ommon Ancestor problem. We thus
More informationMining Social Network Graphs
Mining Social Network Graphs Debapriyo Majumdar Data Mining Fall 2014 Indian Statistical Institute Kolkata November 13, 17, 2014 Social Network No introduc+on required Really? We s7ll need to understand
More informationBig Data from a Database Theory Perspective
Big Data from a Database Theory Perspective Martin Grohe Lehrstuhl Informatik 7  Logic and the Theory of Discrete Systems A CS View on Data Science Applications Data System Users 2 Us Data HUGE heterogeneous
More informationContinuous Fastest Path Planning in Road Networks by Mining RealTime Traffic Event Information
Continuous Fastest Path Planning in Road Networks by Mining RealTime Traffic Event Information Eric HsuehChan Lu ChiWei Huang Vincent S. Tseng Institute of Computer Science and Information Engineering
More informationComputational complexity theory
Computational complexity theory Goal: A general theory of the resources needed to solve computational problems What types of resources? Time What types of computational problems? decision problem Decision
More information2.3 Scheduling jobs on identical parallel machines
2.3 Scheduling jobs on identical parallel machines There are jobs to be processed, and there are identical machines (running in parallel) to which each job may be assigned Each job = 1,,, must be processed
More informationContent Delivery Networks. Shaxun Chen April 21, 2009
Content Delivery Networks Shaxun Chen April 21, 2009 Outline Introduction to CDN An Industry Example: Akamai A Research Example: CDN over Mobile Networks Conclusion Outline Introduction to CDN An Industry
More informationVerifiable Delegation of Computation over Large Datasets
Verifiable Delegation of Computation over Large Datasets Siavosh Benabbas University of Toronto Rosario Gennaro IBM Research Yevgeniy Vahlis AT&T Cloud Computing Data D Code F Y F(D) Cloud could be malicious
More informationBig Data Analytics. Lucas Rego Drumond
Big Data Analytics Lucas Rego Drumond Information Systems and Machine Learning Lab (ISMLL) Institute of Computer Science University of Hildesheim, Germany MapReduce II MapReduce II 1 / 33 Outline 1. Introduction
More informationOn Correlating Performance Metrics
On Correlating Performance Metrics Yiping Ding and Chris Thornley BMC Software, Inc. Kenneth Newman BMC Software, Inc. University of Massachusetts, Boston Performance metrics and their measurements are
More informationLecture 15 An Arithmetic Circuit Lowerbound and Flows in Graphs
CSE599s: Extremal Combinatorics November 21, 2011 Lecture 15 An Arithmetic Circuit Lowerbound and Flows in Graphs Lecturer: Anup Rao 1 An Arithmetic Circuit Lower Bound An arithmetic circuit is just like
More informationSix Degrees of Separation in Online Society
Six Degrees of Separation in Online Society Lei Zhang * TsinghuaSouthampton Joint Lab on Web Science Graduate School in Shenzhen, Tsinghua University Shenzhen, Guangdong Province, P.R.China zhanglei@sz.tsinghua.edu.cn
More information, each of which contains a unique key value, say k i , R 2. such that k i equals K (or to determine that no such record exists in the collection).
The Search Problem 1 Suppose we have a collection of records, say R 1, R 2,, R N, each of which contains a unique key value, say k i. Given a particular key value, K, the search problem is to locate the
More informationMethods & Tools PeertoPeer Jakob Jenkov
Methods & Tools PeertoPeer Jakob Jenkov PeertoPeer (P2P) Definition(s) Potential Routing and Locating Proxy through firewalls and NAT Searching Security Pure P2P There is no central server or router.
More informationChapter 20: Data Analysis
Chapter 20: Data Analysis Database System Concepts, 6 th Ed. See www.dbbook.com for conditions on reuse Chapter 20: Data Analysis Decision Support Systems Data Warehousing Data Mining Classification
More informationParallel Databases. Parallel Architectures. Parallelism Terminology 1/4/2015. Increase performance by performing operations in parallel
Parallel Databases Increase performance by performing operations in parallel Parallel Architectures Shared memory Shared disk Shared nothing closely coupled loosely coupled Parallelism Terminology Speedup:
More information