Selectivity Estimation for Optimizing Similarity Query in Multimedia Databases IDEAL 2003 Paper review

Query optimization in traditional database  Query: find the employee who’s age between and work for Engineering Faculty  Running time of different execution plans depend on  Number of employees between  Number of employees work for Engineering Faculty  Task: Estimate the number in advance and select the best execution plan (selectivity estimation)  Statistics are stored in database (metadata)

Techniques: one dimension  Parametric – unrealistic  Curve fitting – negative value problem  Sampling – large overhead  Non-parametric (Histogram technique) – widely used age

Problem in multimedia database  (Color = ‘red’) ^ (Shape = ‘round’)  Color, shape – feature vector  Multi-dimension  Number of buckets increases exponentially with dimension  Histogram technique fails  1d – 5  2d – 25  3d – 125  4d – 625

Previous Work – SIGMOD 99  Use DCT to compress information of histogram  2D example  Store DCT coefficient DCT Histogram valueDCT coefficients DCT

Reconstruction of histogram value DCT Zone sampling IDCT

Selectivity estimation

Current Work - IDEAL 2003  Extend the range query from hyper-cube to hyper- sphere  Model hyper-sphere as combination of hyper-cube  Task  Find combination of hyper-cubes to represent hyper-sphere  Find the area of overlapping

Generate combination of hyper- cube

Overlapping of hyper-cube with hyper- sphere  Monte-Carlo method  Generate uniformly distributed random point inside the hypercube  Count the number of points within the hyper-sphere  Use the ratio to estimate area of overlapping

Generate uniformly distributed points inside a hyper-sphere  Accept / Reject method  Generate points within hyper-cube  Accept those fall within the hyper-sphere  Greedy method  Generate θ uniformly [0,2π]  Generate r according to F -1 (U(0,1)) θ r

Experiment