Andrew McGregor

Welcome to the Spring 2018 homepage for CMPSCI 711: More Advanced Algorithms.

• Instructor: Andrew McGregor.
  
• Lectures: Tuesday and Thursday, 8:30 to 9:45 am in CMPS 140.
  
• Textbooks:
  • There is no official textbook for the class and all required material will be distributed in class.
  • Background on Randomized Algorithms:
    • Randomized Algorithms by Motwani and Raghavan
    • Probability and Computing by Mitzenmacher and Upfal
    • Concentration of Measure for the Analysis of Randomised Algorithms (Dubhashi, Panconesi)
  • Related Courses:
    • Dartmouth (2015) (Chakrabarti)
    • MIT (2007) (Indyk)
    • Harvard (2017) (Nelson)
    • University of Washington (2014) (Beame)
  • Useful Surveys:
    • Sketch Techniques for Approximate Query Processing (Cormode)
    • Sparse Recovery Using Sparse Matrices (Gilbert, Indyk)
    • Data Streams: Algorithms and Applications (Muthukrishnan)
    • Chapter on Communication Complexity (Arora, Barak)
    • Graph Streaming Algorithms (McGregor)
    • Sketching as a Tool for Numerical Linear Algebra (Woodruff)
  
  
• Homework: Questions: Due 5/1
  
  
• Slides:
  • Course Overview
  • Part 1: Graph Algorithms:
    • Graphs-1: Connectivity, k-connectivity, Spanners, Sparsification
    • Graphs-2: Connectivity via Sketching
    • Graphs-3: Sparsification via Sketching
    • Graphs-4: Insert-Only (Weighted) Matchings
    • Graphs-5: Planar Matchings
    • Graphs-6: Small Matchings
    • Graphs-7: Multiple-Pass Matchings via Multiplicative Weights
    • Graphs-8: Submodular Maximization
    • Graphs-9: Set-Cover and Max Coverage
    • Graphs-10: Correlation Clustering
    • Associated Papers:
      • Analyzing Graph Structure via Linear Measurements (Ahn, Guha, McGregor)
      • On Graph Problems in a Semi-streaming Model (Feigenbaum et al.)
      • Finding Matchings in the Streaming Model (McGregor)
      • A (2+\epsilon)-Approximation for Maximum Weight Matching in the Semi-Streaming Model (Paz and Schwartzman)
      • Streaming Algorithms for Submodular Function Maximization (Chekuri, Gupta, Quanrud)
  • Part 2: Lower Bounds:
    • Lowerbounds-1: Basic Connections, Examples, Hamming Distance
    • Lowerbounds-2: Information Statistics and Disjointness
    • Lowerbounds-3: Greater-Than and Round Elimination
    • Associated Papers:
      • An information statistics approach to data stream and communication complexity (Bar-Yossef, Jayram, Kumar, Sivakumar)
      • The One-Way Communication Complexity of Hamming Distance (Jayram, Kumar, Sivakumar)
  • Part 3: Vectors and Matrices:
    • Vectors-1: Sampling
    • Vectors-2: Intro to Sketches: F0 and F2
    • Vectors-3: Multi-Purpose Sketches: Count-Min, Count-Sketch for Heavy Hitters, Range Queries, Quantiles
    • Vectors-4: Sampling via Sketches: Lp sampling and Applications
    • Vectors-5: Approximate Representations and Signal Reconstruction
    • Vectors-5: Matrix Approximation via Sketches
    • Vectors-5: Least-Squares Regression via Sketches
    • Associated Papers:
      • An Improved Data Stream Summary: The Count-Min Sketch and its Applications (Cormode, Muthukrishnan)
      • The space complexity of approximating the frequency moments (Alon, Matias, Szegedy)
      • Streaming Algorithms from Precision Sampling (Andoni, Krauthgamer, Onak)
      • Tight Bounds for Lp Samplers, Finding Duplicates in Streams, and Related Problems (Jowhari, Sağlam, Tardos)
  Extra Material Slides (not covered in class):
  • Clustering and Geometry:
    • Section 3-1: Coresets and Clustering
    • Section 3-2: Gridbased Sketching
    • Associated Papers:
      • Tight results for clustering and summarizing data streams (Guha)
      • Algorithms for Dynamic Geometric Problems over Data Streams (Indyk)
  • Sequences:
    • Section 4-1: Longest Increasing Sequences and DYCK
    • Section 4-2: Memory Checking
    • Associated Papers:
      • Recognizing well-parenthesized expressions in the streaming model (Magniez, Mathieu, Nayak)
      • Information Cost Tradeoffs for Augmented Index and Streaming Language Recognition (Chakrabarti, Cormode, Kondapally, McGregor)
      • Estimating the Sortedness of a Data Stream (Gopalan, Jayram, Krauthgamer, Kumar)
  • Special Topics:
    • Section 6-1: Sliding Windows
    • Section 6-2: Distributed Streams and Functional Monitoring
    • Section 6-3: Stochastic Streams
    • Associated Papers:
      • Selection and Sorting with Limited Storage (Munro and Paterson)
      • Smooth Histograms for Sliding Windows (Braverman and Ostrovsky)
      • Optimal Random Sampling from Distributed Streams Revisited (Tirthapura and Woodruff)
      • Algorithms for Distributed Functional Monitoring (Cormode, Muthukrishnan, Yi)