RUBIK: Efficient Threshold Queries on Massive Time Series Eleni - PowerPoint PPT Presentation

RUBIK: Efficient Threshold Queries on Massive Time Series Eleni Tzirita Zacharatou ‡ Thomas Heinis* Farhan Tauheed § Anastasia Ailamaki ‡ ‡ École Polytechnique *Imperial College London § Oracle Labs, Zurich Fédérale de Lausanne

Scaling up Brain Simulations voltage Model Resolution time voltage time Temporal Resolution time 3D Neuron Model Time Series Analysis: key to neuroscientific discovery 2

Neuron firing: which and when • Exploration • Identify subsets of interest: time series where voltage > -40 • Hypothesis Testing and time step ∈ [300,400] Threshold Query voltage time Threshold queries fuel efficient data analysis 3

Time Series Correlation… time series id voltage time step Trends Correlation Opportunity to scale with Increased simulation duration Across time increase in temporal resolution Increasingly detailed models Across time series increase in spatial resolution …enables efficient time series-specific compression 4

Time Series Data Discretization Range encoding: Binning: Set bin to ‘1’ if condition satisfied, Partition the values into bins ‘0’ otherwise 3: [15-20) ≥ 20 17 0 0 0 0 2: [10-15) ≥ 15 0 0 1 0 ≥ 10 1: [5-10) 9 5 0 0 1 0 Value ≥ 5 0: [0-5) 2 1 1 1 0 Bin Timestep Timestep Increased similarity Precomputed answers across time series stored as a bitmap 5

Bitmap Compression Today • Run-Length-Encoding compresses each bitvector § Word-Aligned Hybrid Code (WAH) [SSDBM ’02] 4 × ’0’ 0 0 0 0 2 × ’0’, 1 × ’1’, 1 × ‘0’ 0 0 1 0 2 × ’0’, 1 × ’1’, 1 × ‘0’ 0 0 1 0 3 × ’1’, 1 × ‘0’ 1 1 1 0 Bin Timestep • Compression prevents direct access § Timesteps don’t correspond to bit positions 6

Bitmap Compression Today • Run-Length-Encoding compresses each bitvector § Word-Aligned Hybrid Code (WAH) [SSDBM ’02] 4 × ’0’ 0 0 0 0 2 × ’0’, 1 × ’1’, 1 × ‘0’ 0 0 1 0 2 × ’0’, 1 × ’1’, 1 × ‘0’ 0 0 1 0 3 × ’1’, 1 × ‘0’ 1 1 1 0 Bin Timestep • Compression prevents direct access Values filtered independently of timesteps § Timesteps don’t correspond to bit positions Similarities across time series are not exploited 7

Our Approach: RUBIK 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Bitmap index Quadtree-based Bitmap stacking creation bitmap decomposition Access specific Exploit timesteps similarities 8

Quadtree-based 3D Bitmap Decomposition Timestep Start Bins 0 Time series 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 Mix 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 First Split All 0 1 1 All 1 All 1 Mix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 1 0 1 0 0 1 0 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0 1 0 0 0 1 1 0 1 Second Split Mix All 0 All 1 All 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 1 0 9 0

Quadtree-based 3D Bitmap Decomposition Start Mix First Split All 0 All 1 All 1 Mix Second Split Mix All 0 All 1 All 0 0 0 0 0 0 Apply WAH 0 0 1 1 0 0 10

Query Execution Query: Mix voltage > 11 in time steps 1 and 2 All 0 All 1 All 1 Mix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Bin 1 Mix All 0 All 1 All 0 Timestep 1 0 0 1 1 0 1 0 1 0 1 0 1 0 Transformation into a 2D bitmap problem 1 1 1 1 1 0 1 0 One tree traversal to retrieve multiple bitmaps 11

Stacking Time Series Bitmaps Goal: Maximize size and number of common squares bitmap 1 bitmap 3 0 0 0 0 0 0 0 0 bitmap 2 0 1 1 0 1 1 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 Mix Mix Mix All 0 All 1 All 1 All 1 All 1 cluster 1 cluster 2 ⇒ Maximize compression across time series 12

Scaling with Data Volume In-memory indexes: FastBit (WAH-compressed bitmap index) and RUBIK Configuration: 128 bins, Hardware: AMD Opteron CPU @ 2.7GHz, 32GB RAM Time series data: 1000 time steps, 1.2GB – 4.8GB #queries: 60 25 1500 Total execution time (s) FastBit RUBIK FastBit RUBIK 20 1200 Index size (MB) 15 900 10 600 5 300 0 0 312K 624K 1.25M 312K 624K 1.25M # time series # time series RUBIK index size scales 9X to 23X speedup sublinearly 13

RUBIK Sensitivity Analysis Configuration: 128 bins Datasets: 500K – 2M time series, Benchmark: 60 threshold queries, 1024 time steps, 2.1GB – 8.4GB random thresholds, up to 15% selectivity query execution time (s) 2D range query Filtering Index Size Dataset Size 10 8 8 6 size (GB) 6 7.5X 4 4 6.7X 2 2 5.8X 0 0 small medium (2X) large (4X) small medium (2x) large (4x) dataset dataset Increased similarity ⇒ ~80% of the time is spent on Hardware: AMD Opteron, 2.7GHz, 32GB RAM Increased compression filtering 14

Threshold Queries on Time Series • Subsets of interest in neuroscience simulations • RUBIK outperforms state-of-the-art by using: – Quadtree decomposition ⇒ Transformation into a 2D bitmap problem – Time series clustering ⇒ Similarities across time series are exploited • RUBIK scales particularly well with time series from increasingly detailed simulation models Thank you! 15